diff --git a/gpx-rs/src/engine/mod.rs b/gpx-rs/src/engine/mod.rs
index 1fc6822f9..1c2f462ef 100644
--- a/gpx-rs/src/engine/mod.rs
+++ b/gpx-rs/src/engine/mod.rs
@@ -16,8 +16,8 @@ use crate::{
 };
 
 #[derive(Debug, Default)]
-pub struct Engine {
-    history: History,
+pub struct Engine<H: History = GlobalHistory> {
+    history: H,
     selection: Selection,
     order: FileOrder,
     statistics_cache: StatisticsCache,
@@ -29,7 +29,7 @@ pub struct Engine {
     clipboard: Option<Clipboard>,
 }
 
-impl Engine {
+impl<H: History> Engine<H> {
     pub fn statistics(&self) -> &StatisticsBuffer {
         &self.statistics_buffer
     }
@@ -143,13 +143,13 @@ impl Engine {
             .into_iter()
             .map(|file| (file.id, file))
             .collect();
-        let diff = History::diff_between(before.as_ref(), Some(&files));
+        let diff = diff_between(before.as_ref(), Some(&files));
         let mut diff =
             (!(diff.added.is_empty() && diff.removed.is_empty() && diff.modified.is_empty()))
                 .then_some(diff);
         self.categories = restored.categories;
         self.order = FileOrder(restored.order);
-        self.history = History::restored(files);
+        self.history = H::restored(files);
         self.refresh(diff.as_ref());
         sort_diff(&mut diff, &self.order.0);
         Outcome {
@@ -181,14 +181,14 @@ impl Engine {
             })
     }
 
-    /// Whether there is something to undo.
+    /// Whether there is something to undo (for the selected files, with a per-file history).
     pub fn can_undo(&self) -> bool {
-        self.history.can_undo()
+        self.history.can_undo(&self.selection.file_ids())
     }
 
-    /// Whether there is something to redo.
+    /// Whether there is something to redo (for the selected files, with a per-file history).
     pub fn can_redo(&self) -> bool {
-        self.history.can_redo()
+        self.history.can_redo(&self.selection.file_ids())
     }
 
     /// Currently selected elements.
@@ -216,8 +216,8 @@ impl Engine {
         // the files change iff there is a diff, but selection and order actions have none
         let mut diff = match action {
             Action::Edit(command) => self.edit(command)?,
-            Action::Undo => self.history.undo(),
-            Action::Redo => self.history.redo(),
+            Action::Undo => self.history.undo(&self.selection.file_ids()),
+            Action::Redo => self.history.redo(&self.selection.file_ids()),
             Action::Select { selection, mode } => {
                 self.selection
                     .select(self.history.current(), selection, mode);
diff --git a/gpx-rs/src/engine/state/history.rs b/gpx-rs/src/engine/state/history/global.rs
similarity index 68%
rename from gpx-rs/src/engine/state/history.rs
rename to gpx-rs/src/engine/state/history/global.rs
index d8d722983..c91cabfd5 100644
--- a/gpx-rs/src/engine/state/history.rs
+++ b/gpx-rs/src/engine/state/history/global.rs
@@ -1,12 +1,11 @@
-use std::{
-    collections::{HashMap, HashSet},
-    rc::Rc,
-};
+use std::rc::Rc;
 
-use crate::{CommandError, File, FileId};
+use super::{Diff, Files, History, diff_between};
+use crate::{CommandError, FileId};
 
+/// One history for the whole workspace: each entry is a state of all the files.
 #[derive(Debug, Default)]
-pub struct History {
+pub struct GlobalHistory {
     entries: Vec<Files>,
     index: Option<usize>,
     /// Whether the first entry is the state the history starts from, which is not undone: files
@@ -14,37 +13,7 @@ pub struct History {
     floor: bool,
 }
 
-impl History {
-    /// A history whose first entry is `entry`, from which nothing can be undone.
-    pub fn restored(entry: Files) -> Self {
-        Self {
-            entries: vec![entry],
-            index: Some(0),
-            floor: true,
-        }
-    }
-
-    pub fn current(&self) -> Option<&Files> {
-        self.index.map_or_default(|i| self.get(i))
-    }
-
-    /// Applies `f` to a copy of the current entry and makes the copy the new current entry.
-    ///
-    /// Nothing is pushed, and `None` is returned, if `f` fails (the error is returned) or if it
-    /// leaves every file as it was: a step that undoes nothing is not worth a place in the
-    /// history. Files are told apart by their identity, not their content.
-    pub fn create_and_push_next<F>(&mut self, f: F) -> Result<Option<Diff>, CommandError>
-    where
-        F: FnOnce(&mut Files) -> Result<(), CommandError>,
-    {
-        let mut next = self.current().map_or_default(|c| c.clone());
-        f(&mut next)?;
-        if self.is_current(&next) {
-            return Ok(None);
-        }
-        Ok(self.record_diff(|history| history.push(next)))
-    }
-
+impl GlobalHistory {
     /// Whether `entry` holds exactly the files of the current entry.
     fn is_current(&self, entry: &Files) -> bool {
         let current = self.current();
@@ -57,46 +26,6 @@ impl History {
             })
     }
 
-    pub fn undo(&mut self) -> Option<Diff> {
-        self.record_diff(|history| {
-            if let Some(i) = history.index {
-                if i == 0 {
-                    if !history.floor {
-                        history.index = None;
-                    }
-                } else {
-                    history.index = Some(i - 1);
-                }
-            }
-        })
-    }
-
-    pub fn redo(&mut self) -> Option<Diff> {
-        self.record_diff(|history| match history.index {
-            Some(i) => {
-                if i + 1 < history.entries.len() {
-                    history.index = Some(i + 1);
-                }
-            }
-            None => {
-                if !history.entries.is_empty() {
-                    history.index = Some(0);
-                }
-            }
-        })
-    }
-
-    pub fn can_undo(&self) -> bool {
-        self.index.is_some_and(|i| i > 0 || !self.floor)
-    }
-
-    pub fn can_redo(&self) -> bool {
-        match self.index {
-            Some(i) => i + 1 < self.entries.len(),
-            None => !self.entries.is_empty(),
-        }
-    }
-
     fn get(&self, index: usize) -> Option<&Files> {
         self.entries.get(index)
     }
@@ -120,47 +49,86 @@ impl History {
         if prev == cur {
             return None;
         }
-        Some(Self::diff_between(
+        Some(diff_between(
             prev.map_or_default(|i| self.get(i)),
             cur.map_or_default(|i| self.get(i)),
         ))
     }
-
-    /// Which files differ between two states.
-    pub fn diff_between(prev: Option<&Files>, cur: Option<&Files>) -> Diff {
-        let prev_ids: HashSet<FileId> = prev.map_or_default(|e| e.keys().copied().collect());
-        let cur_ids: HashSet<FileId> = cur.map_or_default(|e| e.keys().copied().collect());
-        let mut modified = vec![];
-        for id in prev_ids.intersection(&cur_ids) {
-            let before = prev.map_or_default(|e| e.get(id));
-            let after = cur.map_or_default(|e| e.get(id));
-            if !before.zip(after).is_some_and(|(b, a)| Rc::ptr_eq(b, a)) {
-                modified.push(*id);
-            }
-        }
-        Diff {
-            added: cur_ids.difference(&prev_ids).copied().collect(),
-            removed: prev_ids.difference(&cur_ids).copied().collect(),
-            modified,
-        }
-    }
 }
 
-pub type Files = HashMap<FileId, Rc<File>>;
+impl History for GlobalHistory {
+    fn restored(entry: Files) -> Self {
+        Self {
+            entries: vec![entry],
+            index: Some(0),
+            floor: true,
+        }
+    }
 
-/// Which files were added, removed or modified by a change of the current history entry.
-#[derive(Debug, Default, Clone, PartialEq, Eq)]
-pub struct Diff {
-    pub added: Vec<FileId>,
-    pub removed: Vec<FileId>,
-    pub modified: Vec<FileId>,
+    fn current(&self) -> Option<&Files> {
+        self.index.map_or_default(|i| self.get(i))
+    }
+
+    /// Files are told apart by their identity, not their content.
+    fn create_and_push_next<F>(&mut self, f: F) -> Result<Option<Diff>, CommandError>
+    where
+        F: FnOnce(&mut Files) -> Result<(), CommandError>,
+    {
+        let mut next = self.current().map_or_default(|c| c.clone());
+        f(&mut next)?;
+        if self.is_current(&next) {
+            return Ok(None);
+        }
+        Ok(self.record_diff(|history| history.push(next)))
+    }
+
+    fn undo(&mut self, _files: &[FileId]) -> Option<Diff> {
+        self.record_diff(|history| {
+            if let Some(i) = history.index {
+                if i == 0 {
+                    if !history.floor {
+                        history.index = None;
+                    }
+                } else {
+                    history.index = Some(i - 1);
+                }
+            }
+        })
+    }
+
+    fn redo(&mut self, _files: &[FileId]) -> Option<Diff> {
+        self.record_diff(|history| match history.index {
+            Some(i) => {
+                if i + 1 < history.entries.len() {
+                    history.index = Some(i + 1);
+                }
+            }
+            None => {
+                if !history.entries.is_empty() {
+                    history.index = Some(0);
+                }
+            }
+        })
+    }
+
+    fn can_undo(&self, _files: &[FileId]) -> bool {
+        self.index.is_some_and(|i| i > 0 || !self.floor)
+    }
+
+    fn can_redo(&self, _files: &[FileId]) -> bool {
+        match self.index {
+            Some(i) => i + 1 < self.entries.len(),
+            None => !self.entries.is_empty(),
+        }
+    }
 }
 
 #[cfg(test)]
 mod tests {
     use super::*;
+    use crate::File;
 
-    impl History {
+    impl GlobalHistory {
         /// A step that is expected not to fail.
         fn push_ok(
             &mut self,
@@ -172,10 +140,10 @@ mod tests {
 
     #[test]
     fn test_new_file() {
-        let mut history = History::default();
+        let mut history = GlobalHistory::default();
 
-        assert!(!history.can_undo());
-        assert!(!history.can_redo());
+        assert!(!history.can_undo(&[]));
+        assert!(!history.can_redo(&[]));
         assert!(history.current().is_none());
 
         let diff = history.push_ok(|e| {
@@ -184,8 +152,8 @@ mod tests {
             Ok(())
         });
 
-        assert!(history.can_undo());
-        assert!(!history.can_redo());
+        assert!(history.can_undo(&[]));
+        assert!(!history.can_redo(&[]));
         assert!(history.current().is_some());
 
         assert!(diff.is_some());
@@ -196,7 +164,7 @@ mod tests {
         assert!(diff.modified.is_empty());
     }
 
-    fn add_file(history: &mut History) -> FileId {
+    fn add_file(history: &mut GlobalHistory) -> FileId {
         let file = Rc::new(File::default());
         let id = file.id;
         history
@@ -210,43 +178,43 @@ mod tests {
 
     #[test]
     fn test_failed_command_pushes_nothing() {
-        let mut history = History::default();
+        let mut history = GlobalHistory::default();
         let diff = history.create_and_push_next(|e| {
             e.insert(FileId::default(), Rc::new(File::default()));
             Err(CommandError::InvalidData("nope".to_string()))
         });
         assert_eq!(diff, Err(CommandError::InvalidData("nope".to_string())));
-        assert!(!history.can_undo());
+        assert!(!history.can_undo(&[]));
         assert!(history.current().is_none());
     }
 
     #[test]
     fn test_undo_redo() {
-        let mut history = History::default();
-        assert!(history.undo().is_none());
-        assert!(history.redo().is_none());
+        let mut history = GlobalHistory::default();
+        assert!(history.undo(&[]).is_none());
+        assert!(history.redo(&[]).is_none());
 
         let id = add_file(&mut history);
 
-        let diff = history.undo().unwrap();
+        let diff = history.undo(&[]).unwrap();
         assert_eq!(diff.removed, vec![id]);
         assert!(diff.added.is_empty());
         assert!(history.current().is_none());
-        assert!(!history.can_undo());
-        assert!(history.can_redo());
-        assert!(history.undo().is_none());
+        assert!(!history.can_undo(&[]));
+        assert!(history.can_redo(&[]));
+        assert!(history.undo(&[]).is_none());
 
-        let diff = history.redo().unwrap();
+        let diff = history.redo(&[]).unwrap();
         assert_eq!(diff.added, vec![id]);
         assert!(history.current().unwrap().contains_key(&id));
-        assert!(history.can_undo());
-        assert!(!history.can_redo());
-        assert!(history.redo().is_none());
+        assert!(history.can_undo(&[]));
+        assert!(!history.can_redo(&[]));
+        assert!(history.redo(&[]).is_none());
     }
 
     #[test]
     fn test_modified_and_removed() {
-        let mut history = History::default();
+        let mut history = GlobalHistory::default();
         let id = add_file(&mut history);
 
         let diff = history
@@ -282,13 +250,13 @@ mod tests {
         assert!(history.current().unwrap().is_empty());
 
         // going back restores the renamed file
-        history.undo();
+        history.undo(&[]);
         assert_eq!(history.current().unwrap()[&id].info.name, "renamed");
     }
 
     #[test]
     fn test_a_file_is_modified_when_it_is_not_the_same_one_anymore() {
-        let mut history = History::default();
+        let mut history = GlobalHistory::default();
         let id = add_file(&mut history);
 
         // a copy, even if it has the same content, is another file for the history: files are
@@ -316,17 +284,17 @@ mod tests {
 
     #[test]
     fn test_push_after_undo_drops_redo_branch() {
-        let mut history = History::default();
+        let mut history = GlobalHistory::default();
         let first = add_file(&mut history);
         let second = add_file(&mut history);
 
-        history.undo();
-        assert!(history.can_redo());
+        history.undo(&[]);
+        assert!(history.can_redo(&[]));
         assert!(!history.current().unwrap().contains_key(&second));
 
         let third = add_file(&mut history);
-        assert!(!history.can_redo());
-        assert!(history.redo().is_none());
+        assert!(!history.can_redo(&[]));
+        assert!(history.redo(&[]).is_none());
         let current = history.current().unwrap();
         assert!(current.contains_key(&first));
         assert!(current.contains_key(&third));
@@ -342,24 +310,24 @@ mod tests {
     #[test]
     fn test_restored_history_starts_from_its_entry() {
         let (entry, id) = restored_entry();
-        let mut history = History::restored(entry);
+        let mut history = GlobalHistory::restored(entry);
 
         assert!(history.current().unwrap().contains_key(&id));
         // there is nothing to go back to, nor forward to
-        assert!(!history.can_undo());
-        assert!(!history.can_redo());
-        assert!(history.undo().is_none());
-        assert!(history.redo().is_none());
+        assert!(!history.can_undo(&[]));
+        assert!(!history.can_redo(&[]));
+        assert!(history.undo(&[]).is_none());
+        assert!(history.redo(&[]).is_none());
         assert!(history.current().unwrap().contains_key(&id));
     }
 
     #[test]
     fn test_restored_history_cannot_undo_an_empty_entry_either() {
-        let mut history = History::restored(Files::new());
+        let mut history = GlobalHistory::restored(Files::new());
 
         assert!(history.current().is_some_and(|files| files.is_empty()));
-        assert!(!history.can_undo());
-        assert!(history.undo().is_none());
+        assert!(!history.can_undo(&[]));
+        assert!(history.undo(&[]).is_none());
         // the history is not the one of an engine that has done nothing
         assert!(history.current().is_some());
     }
@@ -367,39 +335,39 @@ mod tests {
     #[test]
     fn test_restored_history_undoes_what_comes_after_it_and_no_further() {
         let (entry, restored) = restored_entry();
-        let mut history = History::restored(entry);
+        let mut history = GlobalHistory::restored(entry);
 
         let added = add_file(&mut history);
-        assert!(history.can_undo());
-        assert!(!history.can_redo());
+        assert!(history.can_undo(&[]));
+        assert!(!history.can_redo(&[]));
         assert_eq!(history.current().unwrap().len(), 2);
 
         // back to the restored files
-        let diff = history.undo().unwrap();
+        let diff = history.undo(&[]).unwrap();
         assert_eq!(diff.removed, vec![added]);
         assert!(diff.added.is_empty() && diff.modified.is_empty());
         assert_eq!(history.current().unwrap().len(), 1);
         assert!(history.current().unwrap().contains_key(&restored));
-        assert!(!history.can_undo());
-        assert!(history.can_redo());
-        assert!(history.undo().is_none());
+        assert!(!history.can_undo(&[]));
+        assert!(history.can_redo(&[]));
+        assert!(history.undo(&[]).is_none());
         assert!(history.current().unwrap().contains_key(&restored));
 
-        let diff = history.redo().unwrap();
+        let diff = history.redo(&[]).unwrap();
         assert_eq!(diff.added, vec![added]);
-        assert!(history.can_undo());
-        assert!(!history.can_redo());
+        assert!(history.can_undo(&[]));
+        assert!(!history.can_redo(&[]));
 
         // and again
-        assert!(history.undo().is_some());
-        assert!(history.undo().is_none());
+        assert!(history.undo(&[]).is_some());
+        assert!(history.undo(&[]).is_none());
         assert!(history.current().unwrap().contains_key(&restored));
     }
 
     #[test]
     fn test_restored_history_removing_its_files_can_be_undone() {
         let (entry, restored) = restored_entry();
-        let mut history = History::restored(entry);
+        let mut history = GlobalHistory::restored(entry);
 
         let diff = history
             .push_ok(|e| {
@@ -410,26 +378,26 @@ mod tests {
         assert_eq!(diff.removed, vec![restored]);
         assert!(history.current().unwrap().is_empty());
 
-        let diff = history.undo().unwrap();
+        let diff = history.undo(&[]).unwrap();
         assert_eq!(diff.added, vec![restored]);
         assert!(history.current().unwrap().contains_key(&restored));
-        assert!(!history.can_undo());
+        assert!(!history.can_undo(&[]));
     }
 
     #[test]
     fn test_restored_history_push_after_undo_drops_redo_branch() {
         let (entry, restored) = restored_entry();
-        let mut history = History::restored(entry);
+        let mut history = GlobalHistory::restored(entry);
         add_file(&mut history);
-        history.undo().unwrap();
-        assert!(history.can_redo());
+        history.undo(&[]).unwrap();
+        assert!(history.can_redo(&[]));
 
         let other = add_file(&mut history);
-        assert!(!history.can_redo());
-        assert!(history.can_undo());
-        let diff = history.undo().unwrap();
+        assert!(!history.can_redo(&[]));
+        assert!(history.can_undo(&[]));
+        let diff = history.undo(&[]).unwrap();
         assert_eq!(diff.removed, vec![other]);
         assert!(history.current().unwrap().contains_key(&restored));
-        assert!(!history.can_undo());
+        assert!(!history.can_undo(&[]));
     }
 }
diff --git a/gpx-rs/src/engine/state/history/mod.rs b/gpx-rs/src/engine/state/history/mod.rs
new file mode 100644
index 000000000..773c7290a
--- /dev/null
+++ b/gpx-rs/src/engine/state/history/mod.rs
@@ -0,0 +1,88 @@
+use std::{
+    collections::{HashMap, HashSet},
+    fmt::Debug,
+    rc::Rc,
+};
+
+use crate::{CommandError, File, FileId};
+
+mod global;
+mod per_file;
+
+pub use global::*;
+pub use per_file::*;
+
+pub type Files = HashMap<FileId, Rc<File>>;
+
+/// What the engine can undo and redo, and the files it holds as a result.
+///
+/// There are two ways to keep it, which the engine can use interchangeably:
+/// - [`GlobalHistory`] has one history for the whole workspace: every step is a state of all the
+///   files, and undoing goes back to the previous one, whatever the files it concerns. Opening and
+///   closing files are steps too.
+/// - [`PerFileHistory`] has one history for each file, which starts when the file appears and ends
+///   when it disappears. Undoing only concerns the files that are asked for, and files appearing
+///   or disappearing are never undone.
+///
+/// Files are told apart by their identity (`Rc::ptr_eq`), not their content.
+pub trait History: Default + Debug {
+    /// A history that starts from `files`, which cannot be undone.
+    fn restored(files: Files) -> Self;
+
+    /// The current state of the files, `None` if there is none yet.
+    fn current(&self) -> Option<&Files>;
+
+    /// Applies `f` to a copy of the current files and makes the copy the new current state.
+    ///
+    /// Nothing is recorded, and `None` is returned, if `f` fails (the error is returned) or if it
+    /// leaves every file as it was: a step that undoes nothing is not worth a place in the history.
+    fn create_and_push_next<F>(&mut self, f: F) -> Result<Option<Diff>, CommandError>
+    where
+        F: FnOnce(&mut Files) -> Result<(), CommandError>;
+
+    /// Goes back one step. A per-file history does it for each of the given `files` (and ignores
+    /// the ones it does not know), a global one ignores them.
+    fn undo(&mut self, files: &[FileId]) -> Option<Diff>;
+
+    /// Goes forward one step, for the same files as [`History::undo`].
+    fn redo(&mut self, files: &[FileId]) -> Option<Diff>;
+
+    /// Whether [`History::undo`] would do something for these `files`.
+    fn can_undo(&self, files: &[FileId]) -> bool;
+
+    /// Whether [`History::redo`] would do something for these `files`.
+    fn can_redo(&self, files: &[FileId]) -> bool;
+}
+
+/// Which files were added, removed or modified by a change of the current files.
+#[derive(Debug, Default, Clone, PartialEq, Eq)]
+pub struct Diff {
+    pub added: Vec<FileId>,
+    pub removed: Vec<FileId>,
+    pub modified: Vec<FileId>,
+}
+
+impl Diff {
+    pub fn is_empty(&self) -> bool {
+        self.added.is_empty() && self.removed.is_empty() && self.modified.is_empty()
+    }
+}
+
+/// Which files differ between two states.
+pub fn diff_between(prev: Option<&Files>, cur: Option<&Files>) -> Diff {
+    let prev_ids: HashSet<FileId> = prev.map_or_default(|e| e.keys().copied().collect());
+    let cur_ids: HashSet<FileId> = cur.map_or_default(|e| e.keys().copied().collect());
+    let mut modified = vec![];
+    for id in prev_ids.intersection(&cur_ids) {
+        let before = prev.map_or_default(|e| e.get(id));
+        let after = cur.map_or_default(|e| e.get(id));
+        if !before.zip(after).is_some_and(|(b, a)| Rc::ptr_eq(b, a)) {
+            modified.push(*id);
+        }
+    }
+    Diff {
+        added: cur_ids.difference(&prev_ids).copied().collect(),
+        removed: prev_ids.difference(&cur_ids).copied().collect(),
+        modified,
+    }
+}
diff --git a/gpx-rs/src/engine/state/history/per_file.rs b/gpx-rs/src/engine/state/history/per_file.rs
new file mode 100644
index 000000000..467519402
--- /dev/null
+++ b/gpx-rs/src/engine/state/history/per_file.rs
@@ -0,0 +1,334 @@
+use std::rc::Rc;
+
+use super::{Diff, Files, History, diff_between};
+use crate::{CommandError, File, FileId};
+
+use std::collections::HashMap;
+
+/// One history for each file, which begins with the state the file appears in (loaded, created,
+/// produced by a command...) and ends when the file disappears: a file coming or going is never
+/// undone, only what happens to it in between.
+#[derive(Debug, Default)]
+pub struct PerFileHistory {
+    current: Files,
+    stacks: HashMap<FileId, FileHistory>,
+}
+
+/// The successive states of a file, the first one being where it starts from.
+#[derive(Debug)]
+struct FileHistory {
+    entries: Vec<Rc<File>>,
+    index: usize,
+}
+
+impl FileHistory {
+    fn new(file: Rc<File>) -> Self {
+        Self {
+            entries: vec![file],
+            index: 0,
+        }
+    }
+
+    fn current(&self) -> &Rc<File> {
+        &self.entries[self.index]
+    }
+
+    fn push(&mut self, file: Rc<File>) {
+        self.entries.truncate(self.index + 1);
+        self.entries.push(file);
+        self.index = self.entries.len() - 1;
+    }
+
+    fn can_undo(&self) -> bool {
+        self.index > 0
+    }
+
+    fn can_redo(&self) -> bool {
+        self.index + 1 < self.entries.len()
+    }
+}
+
+impl PerFileHistory {
+    /// Moves each of the files one step back (`forward` false) or forward, and says which ones
+    /// moved.
+    fn step(&mut self, files: &[FileId], forward: bool) -> Option<Diff> {
+        let mut modified: Vec<FileId> = vec![];
+        for id in files {
+            let Some(history) = self.stacks.get_mut(id) else {
+                continue;
+            };
+            if modified.contains(id) {
+                continue;
+            }
+            if forward && history.can_redo() {
+                history.index += 1;
+            } else if !forward && history.can_undo() {
+                history.index -= 1;
+            } else {
+                continue;
+            }
+            self.current.insert(*id, history.current().clone());
+            modified.push(*id);
+        }
+        (!modified.is_empty()).then(|| Diff {
+            modified,
+            ..Default::default()
+        })
+    }
+
+    fn any(&self, files: &[FileId], f: impl Fn(&FileHistory) -> bool) -> bool {
+        files.iter().any(|id| self.stacks.get(id).is_some_and(&f))
+    }
+}
+
+impl History for PerFileHistory {
+    fn restored(files: Files) -> Self {
+        let stacks = files
+            .iter()
+            .map(|(id, file)| (*id, FileHistory::new(file.clone())))
+            .collect();
+        Self {
+            current: files,
+            stacks,
+        }
+    }
+
+    fn current(&self) -> Option<&Files> {
+        Some(&self.current)
+    }
+
+    fn create_and_push_next<F>(&mut self, f: F) -> Result<Option<Diff>, CommandError>
+    where
+        F: FnOnce(&mut Files) -> Result<(), CommandError>,
+    {
+        let mut next = self.current.clone();
+        f(&mut next)?;
+        let diff = diff_between(Some(&self.current), Some(&next));
+        if diff.is_empty() {
+            return Ok(None);
+        }
+        for id in &diff.removed {
+            self.stacks.remove(id);
+        }
+        for id in &diff.added {
+            self.stacks.insert(*id, FileHistory::new(next[id].clone()));
+        }
+        for id in &diff.modified {
+            match self.stacks.get_mut(id) {
+                Some(history) => history.push(next[id].clone()),
+                None => {
+                    self.stacks.insert(*id, FileHistory::new(next[id].clone()));
+                }
+            }
+        }
+        self.current = next;
+        Ok(Some(diff))
+    }
+
+    fn undo(&mut self, files: &[FileId]) -> Option<Diff> {
+        self.step(files, false)
+    }
+
+    fn redo(&mut self, files: &[FileId]) -> Option<Diff> {
+        self.step(files, true)
+    }
+
+    fn can_undo(&self, files: &[FileId]) -> bool {
+        self.any(files, FileHistory::can_undo)
+    }
+
+    fn can_redo(&self, files: &[FileId]) -> bool {
+        self.any(files, FileHistory::can_redo)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn push(history: &mut PerFileHistory, f: impl FnOnce(&mut Files)) -> Option<Diff> {
+        history
+            .create_and_push_next(|files| {
+                f(files);
+                Ok(())
+            })
+            .unwrap()
+    }
+
+    fn add_file(history: &mut PerFileHistory) -> FileId {
+        let file = Rc::new(File::default());
+        let id = file.id;
+        push(history, |files| {
+            files.insert(id, file);
+        })
+        .unwrap();
+        id
+    }
+
+    fn rename(history: &mut PerFileHistory, id: FileId, name: &str) -> Option<Diff> {
+        push(history, |files| {
+            let mut file = (**files.get(&id).unwrap()).clone();
+            file.info.name = name.to_string();
+            files.insert(id, Rc::new(file));
+        })
+    }
+
+    fn name(history: &PerFileHistory, id: FileId) -> String {
+        history.current().unwrap()[&id].info.name.clone()
+    }
+
+    #[test]
+    fn test_a_new_file_cannot_be_undone() {
+        let mut history = PerFileHistory::default();
+        assert!(history.current().unwrap().is_empty());
+        let id = add_file(&mut history);
+
+        assert!(!history.can_undo(&[id]));
+        assert!(!history.can_redo(&[id]));
+        assert!(history.undo(&[id]).is_none());
+        assert!(history.current().unwrap().contains_key(&id));
+    }
+
+    #[test]
+    fn test_undo_redo_of_a_file() {
+        let mut history = PerFileHistory::default();
+        let id = add_file(&mut history);
+        let before = name(&history, id);
+        let diff = rename(&mut history, id, "renamed").unwrap();
+        assert_eq!(diff.modified, vec![id]);
+        assert!(history.can_undo(&[id]));
+
+        let diff = history.undo(&[id]).unwrap();
+        assert_eq!(diff.modified, vec![id]);
+        assert!(diff.added.is_empty() && diff.removed.is_empty());
+        assert_eq!(name(&history, id), before);
+        assert!(!history.can_undo(&[id]));
+        assert!(history.can_redo(&[id]));
+
+        history.redo(&[id]).unwrap();
+        assert_eq!(name(&history, id), "renamed");
+        assert!(history.redo(&[id]).is_none());
+    }
+
+    #[test]
+    fn test_only_the_given_files_are_undone() {
+        let mut history = PerFileHistory::default();
+        let a = add_file(&mut history);
+        let b = add_file(&mut history);
+        rename(&mut history, a, "a");
+        rename(&mut history, b, "b");
+
+        assert!(history.can_undo(&[a]));
+        assert!(!history.can_undo(&[]));
+        assert!(history.undo(&[]).is_none());
+
+        let diff = history.undo(&[a]).unwrap();
+        assert_eq!(diff.modified, vec![a]);
+        assert_ne!(name(&history, a), "a");
+        assert_eq!(name(&history, b), "b");
+        // a has nothing more to undo, b still has
+        assert!(!history.can_undo(&[a]));
+        assert!(history.can_undo(&[a, b]));
+        assert!(history.undo(&[a]).is_none());
+    }
+
+    #[test]
+    fn test_several_files_are_undone_each_by_its_own_step() {
+        let mut history = PerFileHistory::default();
+        let a = add_file(&mut history);
+        let b = add_file(&mut history);
+        rename(&mut history, a, "a1");
+        rename(&mut history, a, "a2");
+        rename(&mut history, b, "b1");
+
+        let diff = history.undo(&[a, b, a]).unwrap();
+        assert_eq!(diff.modified, vec![a, b]);
+        // a is only moved once, even if it is asked for twice
+        assert_eq!(name(&history, a), "a1");
+        assert_ne!(name(&history, b), "b1");
+    }
+
+    #[test]
+    fn test_a_step_after_an_undo_drops_the_redo_branch_of_that_file_only() {
+        let mut history = PerFileHistory::default();
+        let a = add_file(&mut history);
+        let b = add_file(&mut history);
+        rename(&mut history, a, "a1");
+        rename(&mut history, b, "b1");
+        history.undo(&[a, b]).unwrap();
+
+        rename(&mut history, a, "a2");
+        assert!(!history.can_redo(&[a]));
+        assert!(history.can_redo(&[b]));
+    }
+
+    #[test]
+    fn test_a_step_that_changes_nothing_is_not_recorded() {
+        let mut history = PerFileHistory::default();
+        let id = add_file(&mut history);
+        assert!(push(&mut history, |_| {}).is_none());
+        assert!(!history.can_undo(&[id]));
+    }
+
+    #[test]
+    fn test_failed_command_pushes_nothing() {
+        let mut history = PerFileHistory::default();
+        let id = add_file(&mut history);
+        let result = history.create_and_push_next(|files| {
+            files.remove(&id);
+            Err(CommandError::InvalidData("nope".to_string()))
+        });
+        assert_eq!(result, Err(CommandError::InvalidData("nope".to_string())));
+        assert!(history.current().unwrap().contains_key(&id));
+    }
+
+    #[test]
+    fn test_removing_a_file_drops_its_history() {
+        let mut history = PerFileHistory::default();
+        let id = add_file(&mut history);
+        rename(&mut history, id, "renamed");
+
+        let diff = push(&mut history, |files| {
+            files.remove(&id);
+        })
+        .unwrap();
+        assert_eq!(diff.removed, vec![id]);
+        assert!(history.current().unwrap().is_empty());
+        assert!(!history.can_undo(&[id]));
+        assert!(history.undo(&[id]).is_none());
+        assert!(history.current().unwrap().is_empty());
+    }
+
+    #[test]
+    fn test_a_file_that_comes_back_starts_over() {
+        let mut history = PerFileHistory::default();
+        let file = Rc::new(File::default());
+        let id = file.id;
+        push(&mut history, |files| {
+            files.insert(id, file.clone());
+        });
+        rename(&mut history, id, "renamed");
+        push(&mut history, |files| {
+            files.remove(&id);
+        });
+        push(&mut history, |files| {
+            files.insert(id, file.clone());
+        });
+        assert!(!history.can_undo(&[id]));
+    }
+
+    #[test]
+    fn test_restored_files_cannot_be_undone() {
+        let file = Rc::new(File::default());
+        let id = file.id;
+        let mut history = PerFileHistory::restored(Files::from([(id, file)]));
+        assert!(history.current().unwrap().contains_key(&id));
+        assert!(!history.can_undo(&[id]));
+        assert!(history.undo(&[id]).is_none());
+
+        rename(&mut history, id, "renamed");
+        assert!(history.can_undo(&[id]));
+        history.undo(&[id]).unwrap();
+        assert!(!history.can_undo(&[id]));
+    }
+}
diff --git a/gpx-rs/src/engine/state/selection.rs b/gpx-rs/src/engine/state/selection.rs
index bbd7cc108..8d24a3c7d 100644
--- a/gpx-rs/src/engine/state/selection.rs
+++ b/gpx-rs/src/engine/state/selection.rs
@@ -312,6 +312,14 @@ fn neighbour<T: Copy + PartialEq + std::hash::Hash + Eq>(
 }
 
 impl Selection {
+    /// The ids of the files holding the selected elements.
+    pub fn file_ids(&self) -> Vec<FileId> {
+        match self.to_files() {
+            Selection::File { file_ids } => file_ids.into_iter().collect(),
+            _ => vec![],
+        }
+    }
+
     /// The files holding the selected elements, as a selection of files.
     pub fn to_files(&self) -> Selection {
         match self {
diff --git a/gpx-rs/src/engine/tests.rs b/gpx-rs/src/engine/tests.rs
index 5f622cef9..dc3015851 100644
--- a/gpx-rs/src/engine/tests.rs
+++ b/gpx-rs/src/engine/tests.rs
@@ -153,7 +153,7 @@ fn test_invalid_load_is_rejected() {
         })
     ));
     assert!(engine.history.current().is_none());
-    assert!(!engine.history.can_undo());
+    assert!(!engine.history.can_undo(&[]));
     assert!(engine.order.0.is_empty());
 }
 
@@ -162,7 +162,7 @@ fn test_command_with_nothing_to_do_is_rejected() {
     let mut engine = TestEngine::default();
     new(&mut engine, "file");
     assert!(!edit(&mut engine, Command::Reverse(crate::Reverse)));
-    assert!(!engine.history.can_redo());
+    assert!(!engine.history.can_redo(&[]));
     assert_eq!(engine.history.current().unwrap().len(), 1);
 }
 
@@ -1434,3 +1434,106 @@ fn test_overwriting_forgets_the_history() {
     engine.restore(restored_from(&engine, &ids, vec![]));
     assert!(!engine.can_undo());
 }
+
+mod per_file_history {
+    use super::*;
+
+    fn new_file(engine: &mut Engine<PerFileHistory>, name: &str) -> FileId {
+        engine
+            .execute(Action::Edit(Command::New(New {
+                name,
+                trackpoint: None,
+            })))
+            .unwrap();
+        *engine.order().last().unwrap()
+    }
+
+    fn select(engine: &mut Engine<PerFileHistory>, ids: &[FileId]) {
+        engine
+            .execute(Action::Select {
+                selection: Selection::File {
+                    file_ids: ids.iter().copied().collect(),
+                },
+                mode: SelectMode::Replace,
+            })
+            .unwrap();
+    }
+
+    fn rename(engine: &mut Engine<PerFileHistory>, name: &str) {
+        engine
+            .execute(Action::Edit(Command::Metadata(Metadata { name, desc: "" })))
+            .unwrap();
+    }
+
+    fn name_of(engine: &Engine<PerFileHistory>, id: FileId) -> String {
+        engine.file_structure(&id).unwrap().name.clone()
+    }
+
+    #[test]
+    fn test_creating_a_file_is_not_undoable() {
+        let mut engine = Engine::<PerFileHistory>::default();
+        let id = new_file(&mut engine, "file");
+        assert!(!engine.can_undo());
+        assert!(!engine.execute(Action::Undo).unwrap().changed);
+        assert_eq!(engine.order(), [id]);
+    }
+
+    #[test]
+    fn test_undo_follows_the_selected_files() {
+        let mut engine = Engine::<PerFileHistory>::default();
+        let a = new_file(&mut engine, "a");
+        let b = new_file(&mut engine, "b");
+
+        select(&mut engine, &[a]);
+        rename(&mut engine, "a2");
+        select(&mut engine, &[b]);
+        rename(&mut engine, "b2");
+
+        // b is selected: only its change is undone
+        assert!(engine.can_undo());
+        let outcome = engine.execute(Action::Undo).unwrap();
+        assert_eq!(outcome.diff.unwrap().modified, vec![b]);
+        assert_eq!(name_of(&engine, b), "b");
+        assert_eq!(name_of(&engine, a), "a2");
+        assert!(!engine.can_undo());
+        assert!(engine.can_redo());
+
+        select(&mut engine, &[a]);
+        assert!(engine.can_undo());
+        assert!(!engine.can_redo());
+        engine.execute(Action::Undo).unwrap();
+        assert_eq!(name_of(&engine, a), "a");
+
+        select(&mut engine, &[b]);
+        engine.execute(Action::Redo).unwrap();
+        assert_eq!(name_of(&engine, b), "b2");
+    }
+
+    #[test]
+    fn test_undo_without_selection_does_nothing() {
+        let mut engine = Engine::<PerFileHistory>::default();
+        new_file(&mut engine, "a");
+        rename(&mut engine, "a2");
+        engine
+            .execute(Action::Select {
+                selection: Selection::Empty,
+                mode: SelectMode::Replace,
+            })
+            .unwrap();
+        assert!(!engine.can_undo());
+        assert!(!engine.execute(Action::Undo).unwrap().changed);
+    }
+
+    #[test]
+    fn test_deleting_a_file_drops_its_history() {
+        let mut engine = Engine::<PerFileHistory>::default();
+        let id = new_file(&mut engine, "a");
+        rename(&mut engine, "a2");
+        engine
+            .execute(Action::Edit(Command::Delete(Delete { whole_files: false })))
+            .unwrap();
+        assert!(engine.order().is_empty());
+        assert!(!engine.execute(Action::Undo).unwrap().changed);
+        assert!(engine.file_structure(&id).is_none());
+    }
+}