diff --git a/gpx-rs/engine/src/engine/engine.rs b/gpx-rs/engine/src/engine/engine.rs
index 9a6e8c319..929bafb92 100644
--- a/gpx-rs/engine/src/engine/engine.rs
+++ b/gpx-rs/engine/src/engine/engine.rs
@@ -17,6 +17,7 @@ pub struct Engine {
     structure_cache: FileStructureCache,
     diff: Option<Diff>,
     order_changed: bool,
+    selection_changed: bool,
     statistics_buffer: StatisticsBuffer,
 }
 
@@ -45,6 +46,16 @@ impl Engine {
         self.order_changed
     }
 
+    /// Currently selected elements.
+    pub fn selection(&self) -> &Selection {
+        &self.selection
+    }
+
+    /// Whether the last action changed the selection.
+    pub fn selection_changed(&self) -> bool {
+        self.selection_changed
+    }
+
     /// Coordinates (`[lng, lat, ...]`) of the trackpoints of a segment.
     pub fn segment_coordinates(&self, id: &TrackSegmentId) -> &[f64] {
         self.coordinates_cache.segment(id)
@@ -93,12 +104,15 @@ impl Engine {
                 None
             }
         };
-        let selection_changed = self.selection != selection_before;
-        self.order_changed = self.order.0 != order_before;
-        let changed = self.diff.is_some() || selection_changed || self.order_changed;
+        let changed = self.diff.is_some()
+            || self.selection != selection_before
+            || self.order.0 != order_before;
         if changed {
             self.refresh();
         }
+        // after the refresh, which also syncs the order and selection with the files (undo, redo)
+        self.order_changed = self.order.0 != order_before;
+        self.selection_changed = self.selection != selection_before;
         changed
     }
 
@@ -374,6 +388,7 @@ mod tests {
         assert!(diff.is_some());
         let diff = diff.as_ref().unwrap();
         assert_eq!(diff.removed, vec![empty_id]);
+        assert!(engine.order_changed());
         assert!(engine.file_structure(&empty_id).is_none());
         assert!(engine.execute(Action::Undo));
         assert!(engine.order().is_empty());
@@ -381,6 +396,24 @@ mod tests {
         assert!(engine.segment_coordinates(&seg_id).is_empty());
     }
 
+    #[test]
+    fn test_selection_changed_flag() {
+        let mut engine = Engine::default();
+        new(&mut engine, "a");
+        let a = engine.order()[0];
+        // a new file is selected by the edit
+        assert!(engine.selection_changed());
+        assert!(!engine.execute(Action::Select { file_ids: vec![a] }));
+        assert!(!engine.selection_changed());
+        assert!(engine.execute(Action::Select { file_ids: vec![] }));
+        assert!(engine.selection_changed());
+        // undoing drops the selected file from the selection
+        engine.execute(Action::Select { file_ids: vec![a] });
+        assert!(engine.execute(Action::Undo));
+        assert!(engine.selection_changed());
+        assert_eq!(engine.selection(), &Selection::Empty);
+    }
+
     #[test]
     fn test_undo_updates_statistics() {
         let mut engine = Engine::default();
diff --git a/gpx-rs/wasm/src/lib.rs b/gpx-rs/wasm/src/lib.rs
index b66165ccd..4dbbb689a 100644
--- a/gpx-rs/wasm/src/lib.rs
+++ b/gpx-rs/wasm/src/lib.rs
@@ -332,8 +332,16 @@ pub fn select_all() -> bool {
 
 #[wasm_bindgen(typescript_custom_section)]
 const FILE_STRUCTURE_TS: &str = r#"
+export type Selection =
+    | { type: 'empty' }
+    | { type: 'file'; fileIds: string[] }
+    | { type: 'track'; fileId: string; trackIds: string[] }
+    | { type: 'segment'; fileId: string; trackId: string; segmentIds: string[] }
+    | { type: 'waypoints'; fileId: string }
+    | { type: 'waypoint'; fileId: string; waypointIds: string[] };
 export interface FilesUpdate {
     orderChanged: boolean;
+    selectionChanged: boolean;
     /** Files to read the structure of. */
     added: string[];
     /** Files whose structure changed: reread it. */
@@ -369,6 +377,8 @@ export interface WaypointNode {
 
 #[wasm_bindgen]
 extern "C" {
+    #[wasm_bindgen(typescript_type = "Selection")]
+    pub type Selection;
     #[wasm_bindgen(typescript_type = "FilesUpdate")]
     pub type FilesUpdate;
     #[wasm_bindgen(typescript_type = "FileStructure | undefined")]
@@ -452,6 +462,52 @@ pub fn file_structure(file_id: &str) -> FileStructure {
     structure.unchecked_into()
 }
 
+fn uuids<T>(items: impl IntoIterator<Item = T>, uuid: impl Fn(T) -> uuid::Uuid) -> Array {
+    items
+        .into_iter()
+        .map(|item| JsValue::from(uuid(item).to_string()))
+        .collect()
+}
+
+/// The current selection (ids are UUID strings).
+#[wasm_bindgen]
+pub fn selection() -> Selection {
+    use engine::Selection as S;
+    let object = Object::new();
+    with_engine(|e| match e.selection() {
+        S::Empty => set(&object, "type", "empty"),
+        S::File { file_ids } => {
+            set(&object, "type", "file");
+            set(&object, "fileIds", uuids(file_ids, |id| id.0));
+        }
+        S::Track { file_id, trk_ids } => {
+            set(&object, "type", "track");
+            set(&object, "fileId", file_id.0.to_string());
+            set(&object, "trackIds", uuids(trk_ids, |id| id.0));
+        }
+        S::TrackSegment {
+            file_id,
+            trk_id,
+            trkseg_ids,
+        } => {
+            set(&object, "type", "segment");
+            set(&object, "fileId", file_id.0.to_string());
+            set(&object, "trackId", trk_id.0.to_string());
+            set(&object, "segmentIds", uuids(trkseg_ids, |id| id.0));
+        }
+        S::Waypoints { file_id } => {
+            set(&object, "type", "waypoints");
+            set(&object, "fileId", file_id.0.to_string());
+        }
+        S::Waypoint { file_id, wpt_ids } => {
+            set(&object, "type", "waypoint");
+            set(&object, "fileId", file_id.0.to_string());
+            set(&object, "waypointIds", uuids(wpt_ids, |id| id.0));
+        }
+    });
+    object.unchecked_into()
+}
+
 /// What the last action changed. Read it right after each action.
 #[wasm_bindgen]
 pub fn last_update() -> FilesUpdate {
@@ -459,6 +515,7 @@ pub fn last_update() -> FilesUpdate {
     with_engine(|e| {
         let diff = e.last_diff().clone().unwrap_or_default();
         set(&update, "orderChanged", e.order_changed());
+        set(&update, "selectionChanged", e.selection_changed());
         set(&update, "added", ids(&diff.added));
         set(&update, "modified", ids(&diff.modified));
         set(&update, "removed", ids(&diff.removed));
diff --git a/website/src/lib/engine.ts b/website/src/lib/engine.ts
index 95e5517ce..3e41c7a09 100644
--- a/website/src/lib/engine.ts
+++ b/website/src/lib/engine.ts
@@ -1,21 +1,152 @@
-import { writable, type Subscriber, type Writable } from 'svelte/store';
+import { browser } from '$app/environment';
+import { writable, type Readable } from 'svelte/store';
+import type { FileStructure, Selection } from 'gpx-rs';
 
+export type {
+    FileStructure,
+    FilesUpdate,
+    Selection,
+    TrackNode,
+    SegmentNode,
+    WaypointNode,
+} from 'gpx-rs';
+
+type Wasm = typeof import('gpx-rs');
+
+/** Hyphenated UUID strings (as found in the file structures) to the concatenated 16-byte form. */
+function idsToBytes(ids: string[]): Uint8Array {
+    const bytes = new Uint8Array(ids.length * 16);
+    ids.forEach((id, i) => {
+        const hex = id.replaceAll('-', '');
+        for (let j = 0; j < 16; j++) {
+            bytes[i * 16 + j] = parseInt(hex.slice(2 * j, 2 * j + 2), 16);
+        }
+    });
+    return bytes;
+}
+
+/**
+ * Thin wrapper around the WASM engine.
+ *
+ * The engine owns the files; this class mirrors what the UI needs in stores. After each action,
+ * only what the engine reports as changed is read again: the order of the files, and the
+ * structure of the files that were added or modified.
+ */
 class Engine {
-    _engine: Writable<any>;
+    private wasm: Wasm | null = null;
+    /** Resolves once the engine can be used (never on the server). */
+    readonly ready: Promise<void>;
+
+    private _order = writable<string[]>([]);
+    private _structures = writable<Map<string, FileStructure>>(new Map());
+    private _selection = writable<Selection>({ type: 'empty' });
+
+    /** Ids of the files in display order. */
+    readonly order: Readable<string[]> = { subscribe: this._order.subscribe };
+    /** What is currently selected. */
+    readonly selection: Readable<Selection> = { subscribe: this._selection.subscribe };
+    /** Structure (names, tracks, segments, waypoints and their ids) of each file. */
+    readonly structures: Readable<Map<string, FileStructure>> = {
+        subscribe: this._structures.subscribe,
+    };
 
     constructor() {
-        this._engine = writable(null);
-        import('gpx-rs').then((wasm) => {
-            this._engine.set(new wasm.Engine(this.onUpdate));
-        });
+        this.ready = browser
+            ? import('gpx-rs').then((wasm) => {
+                  wasm.start();
+                  this.wasm = wasm;
+              })
+            : new Promise(() => {});
     }
 
-    subscribe(run: Subscriber<any>, invalidate?: () => void) {
-        return this._engine.subscribe(run, invalidate);
+    // Actions. Each one resolves to whether the engine changed something.
+
+    newFile(name: string) {
+        return this.run((w) => w.new_file(name));
     }
 
-    onUpdate(message: String) {
-        console.log('message from WASM: ' + message);
+    loadFile(data: Uint8Array) {
+        return this.run((w) => w.load_file(data));
+    }
+
+    duplicate() {
+        return this.run((w) => w.duplicate());
+    }
+
+    delete() {
+        return this.run((w) => w._delete());
+    }
+
+    deleteAll() {
+        return this.run((w) => w.delete_all());
+    }
+
+    undo() {
+        return this.run((w) => w.undo());
+    }
+
+    redo() {
+        return this.run((w) => w.redo());
+    }
+
+    select(fileIds: string[]) {
+        return this.run((w) => w.select(idsToBytes(fileIds)));
+    }
+
+    addSelect(fileIds: string[]) {
+        return this.run((w) => w.add_select(idsToBytes(fileIds)));
+    }
+
+    selectAll() {
+        return this.run((w) => w.select_all());
+    }
+
+    /** Moves the files, in the given order, to `index` among the other files. */
+    reorder(fileIds: string[], index: number) {
+        return this.run((w) => w.reorder(idsToBytes(fileIds), index));
+    }
+
+    // Coordinates, as flat [lng, lat, ...] arrays. They are copied out of the WASM memory.
+    // Refetch them when the `rev` of the segment (or the `waypointsRev` of the file) changed.
+
+    segmentCoordinates(segmentId: string): Float64Array {
+        return this.wasm?.segment_coordinates(segmentId).slice() ?? new Float64Array();
+    }
+
+    waypointCoordinates(fileId: string): Float64Array {
+        return this.wasm?.waypoint_coordinates(fileId).slice() ?? new Float64Array();
+    }
+
+    private async run(action: (wasm: Wasm) => boolean): Promise<boolean> {
+        await this.ready;
+        const wasm = this.wasm!;
+        const changed = action(wasm);
+        this.sync(wasm);
+        return changed;
+    }
+
+    /** Reads what the last action changed. */
+    private sync(wasm: Wasm) {
+        const update = wasm.last_update();
+        if (update.selectionChanged) {
+            this._selection.set(wasm.selection());
+        }
+        if (update.orderChanged) {
+            this._order.set(wasm.file_order());
+        }
+        if (update.added.length + update.modified.length + update.removed.length > 0) {
+            this._structures.update((structures) => {
+                const next = new Map(structures);
+                update.removed.forEach((id) => next.delete(id));
+                [...update.added, ...update.modified].forEach((id) => {
+                    const structure = wasm.file_structure(id);
+                    if (structure) {
+                        next.set(id, structure);
+                    }
+                });
+                return next;
+            });
+        }
     }
 }