diff --git a/app/client/components/CustomView.ts b/app/client/components/CustomView.ts
index ae14ed61..32f1b019 100644
--- a/app/client/components/CustomView.ts
+++ b/app/client/components/CustomView.ts
@@ -3,6 +3,7 @@ import * as commands from 'app/client/components/commands';
 import {Cursor} from 'app/client/components/Cursor';
 import {GristDoc} from 'app/client/components/GristDoc';
 import {
+  CommandAPI,
   ConfigNotifier,
   CustomSectionAPIImpl,
   GristDocAPIImpl,
@@ -240,6 +241,10 @@ export class CustomView extends Disposable {
             access,
             this._promptAccess.bind(this)),
           new MinimumLevel(AccessLevel.none));
+        frame.exposeAPI(
+          "CommandAPI",
+          new CommandAPI(access),
+          new MinimumLevel(AccessLevel.none));
         frame.useEvents(RecordNotifier.create(frame, view), new MinimumLevel(AccessLevel.read_table));
         frame.useEvents(TableNotifier.create(frame, view), new MinimumLevel(AccessLevel.read_table));
         frame.exposeAPI(
diff --git a/app/client/components/WidgetFrame.ts b/app/client/components/WidgetFrame.ts
index 731b57a4..6c08d5c7 100644
--- a/app/client/components/WidgetFrame.ts
+++ b/app/client/components/WidgetFrame.ts
@@ -1,4 +1,6 @@
 import BaseView from 'app/client/components/BaseView';
+import {CommandName} from 'app/client/components/commandList';
+import * as commands from 'app/client/components/commands';
 import {GristDoc} from 'app/client/components/GristDoc';
 import {hooks} from 'app/client/Hooks';
 import {get as getBrowserGlobals} from 'app/client/lib/browserGlobals';
@@ -484,6 +486,26 @@ export class WidgetAPIImpl implements WidgetAPI {
   }
 }
 
+const COMMAND_MINIMUM_ACCESS_LEVELS: Map<CommandName, AccessLevel> = new Map([
+  ['undo', AccessLevel.full],
+  ['redo', AccessLevel.full],
+]);
+
+export class CommandAPI {
+  constructor(private _currentAccess: AccessLevel) {}
+
+  public async run(commandName: CommandName): Promise<unknown> {
+    const minimumAccess = COMMAND_MINIMUM_ACCESS_LEVELS.get(commandName);
+    if (minimumAccess === undefined || !isSatisfied(this._currentAccess, minimumAccess)) {
+      // If the command name is unrecognized, or the current access level doesn't meet the
+      // command's minimum access level, do nothing.
+      return;
+    }
+
+    return await commands.allCommands[commandName].run();
+  }
+}
+
 /************************
  * Events that are sent to the CustomWidget.
  *
diff --git a/app/plugin/grist-plugin-api.ts b/app/plugin/grist-plugin-api.ts
index f617b33e..9c3fbf51 100644
--- a/app/plugin/grist-plugin-api.ts
+++ b/app/plugin/grist-plugin-api.ts
@@ -65,6 +65,8 @@ export const widgetApi = rpc.getStub<WidgetAPI>('WidgetAPI', checkers.WidgetAPI)
  */
 export const sectionApi = rpc.getStub<CustomSectionAPI>('CustomSectionAPI', checkers.CustomSectionAPI);
 
+export const commandApi = rpc.getStub<any>('CommandAPI');
+
 /**
  * Shortcut for [[GristView.allowSelectBy]].
  */
@@ -437,6 +439,12 @@ export async function addImporter(name: string, path: string, mode: 'fullscreen'
   });
 }
 
+export function enableKeyboardShortcuts() {
+  const Mousetrap = require('mousetrap');
+  Mousetrap.bind('mod+z', () => commandApi.run('undo'));
+  Mousetrap.bind(['mod+shift+z', 'ctrl+y'], () => commandApi.run('redo'));
+}
+
 /**
  * Options when initializing connection to Grist.
  */
diff --git a/package.json b/package.json
index 3a6c451d..21eabdb8 100644
--- a/package.json
+++ b/package.json
@@ -66,6 +66,7 @@
     "@types/minio": "7.0.15",
     "@types/mocha": "5.2.5",
     "@types/moment-timezone": "0.5.9",
+    "@types/mousetrap": "1.6.2",
     "@types/node": "^14",
     "@types/node-fetch": "2.6.2",
     "@types/pidusage": "2.0.1",
diff --git a/static/custom-widget.html b/static/custom-widget.html
index f7492ae6..c01c8764 100644
--- a/static/custom-widget.html
+++ b/static/custom-widget.html
@@ -7,6 +7,7 @@
   <script src="/grist-plugin-api.js"></script>
   <script>
     grist.ready();
+    grist.enableKeyboardShortcuts();
   </script>
   <style>
     body {
diff --git a/test/fixtures/sites/readout/page.js b/test/fixtures/sites/readout/page.js
index dd466612..6a870192 100644
--- a/test/fixtures/sites/readout/page.js
+++ b/test/fixtures/sites/readout/page.js
@@ -32,6 +32,7 @@ function setup() {
   grist.onNewRecord(function(rec) {
     document.getElementById('record').innerHTML = 'new';
   });
+  grist.enableKeyboardShortcuts();
 }
 
 window.onload = setup;
diff --git a/test/nbrowser/CustomView.ts b/test/nbrowser/CustomView.ts
index 5919d96a..80bc28fc 100644
--- a/test/nbrowser/CustomView.ts
+++ b/test/nbrowser/CustomView.ts
@@ -236,6 +236,31 @@ describe('CustomView', function() {
         await gu.undo();
       });
 
+      const undoTestTitle = access === 'full'
+        ? 'allows undo/redo via keyboard'
+        : 'does not allow undo/redo via keyboard';
+      it (undoTestTitle, async function() {
+        const iframe = gu.getSection('Friends custom').find('iframe');
+        await driver.switchTo().frame(iframe);
+        await driver.find('body').click();
+
+        await gu.sendKeys(Key.chord(Key.CONTROL, 'y'));
+        const expected = access === 'full'
+          ? withAccess(['Rabbit', 'Tom', 'Sydney', 'Bill', 'Evan', 'Mary'], undefined)
+          : withAccess(['Roger', 'Tom', 'Sydney', 'Bill', 'Evan', 'Mary'], undefined);
+        await gu.waitToPass(async () => {
+          assert.deepEqual(readJson(await driver.find('#placeholder').getText())?.Name, expected);
+        }, 1000);
+
+        await gu.sendKeys(Key.chord(await gu.modKey(), 'z'));
+        await gu.waitToPass(async () => {
+          assert.deepEqual(readJson(await driver.find('#placeholder').getText())?.Name,
+          withAccess(['Roger', 'Tom', 'Sydney', 'Bill', 'Evan', 'Mary'], undefined));
+        }, 1000);
+
+        await driver.switchTo().defaultContent();
+      });
+
       it('allows switching to custom section by clicking inside it', async function() {
         await gu.getCell({section: 'FRIENDS', col: 0, rowNum: 1}).click();
         assert.equal(await gu.getActiveSectionTitle(), 'FRIENDS');
@@ -245,7 +270,7 @@ describe('CustomView', function() {
         await driver.switchTo().frame(iframe);
         await driver.find('body').click();
 
-        // Check that the right secton is active, and its settings visible in the side panel.
+        // Check that the right section is active, and its settings visible in the side panel.
         await driver.switchTo().defaultContent();
         assert.equal(await gu.getActiveSectionTitle(), 'FRIENDS Custom');
         assert.equal(await driver.find('.test-config-widget-url').isPresent(), true);
diff --git a/yarn.lock b/yarn.lock
index 158b1b93..3f82821d 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -843,6 +843,11 @@
   dependencies:
     moment ">=2.14.0"
 
+"@types/mousetrap@1.6.2":
+  version "1.6.2"
+  resolved "https://registry.yarnpkg.com/@types/mousetrap/-/mousetrap-1.6.2.tgz#5f48bdbd28c8a447167263ae436488f1d8be072d"
+  integrity sha512-m67PUdzoHJGmYJ6Fno4iXocl+azw9cuz8tdUG21M04UzMRUT1YfxPIIIt3lQkXLMGwlGSKXYNGxCOMxKlGegIw==
+
 "@types/node-fetch@2.6.2":
   version "2.6.2"
   resolved "https://registry.yarnpkg.com/@types/node-fetch/-/node-fetch-2.6.2.tgz#d1a9c5fd049d9415dce61571557104dec3ec81da"