diff --git a/src/components/Tooltip/Tooltip.test.tsx b/src/components/Tooltip/Tooltip.test.tsx
index 45520d14..d517232a 100644
--- a/src/components/Tooltip/Tooltip.test.tsx
+++ b/src/components/Tooltip/Tooltip.test.tsx
@@ -1,5 +1,5 @@
 /*
-Copyright 2023 New Vector Ltd
+Copyright 2023-2024 New Vector Ltd
 
 Licensed under the Apache License, Version 2.0 (the "License");
 you may not use this file except in compliance with the License.
@@ -14,9 +14,9 @@ See the License for the specific language governing permissions and
 limitations under the License.
 */
 
-import { describe, it, expect } from "vitest";
-import { render, screen } from "@testing-library/react";
-import React from "react";
+import { describe, it, expect, vi } from "vitest";
+import { fireEvent, render, screen } from "@testing-library/react";
+import React, { act } from "react";
 
 import * as stories from "./Tooltip.stories";
 import { composeStories, composeStory } from "@storybook/react";
@@ -37,6 +37,19 @@ const {
   Descriptive,
 } = composeStories(stories);
 
+/**
+ * Patches an element to always match :focus-visible whenever it's in focus.
+ * JSDOM doesn't seem to support this selector on its own.
+ */
+function mockFocusVisible(e: Element): void {
+  const originalMatches = e.matches.bind(e);
+  vi.spyOn(e, "matches").mockImplementation(
+    (selectors) =>
+      originalMatches(selectors) ||
+      (selectors === ":focus-visible" && e === document.activeElement),
+  );
+}
+
 describe("Tooltip", () => {
   it("renders open by default", () => {
     render(<ForcedOpen />);
@@ -69,6 +82,7 @@ describe("Tooltip", () => {
   it("opens tooltip on focus", async () => {
     const user = userEvent.setup();
     render(<InteractiveTrigger />);
+    mockFocusVisible(screen.getByRole("link"));
     expect(screen.queryByRole("tooltip")).toBe(null);
     await user.tab();
     // trigger focused, tooltip shown
@@ -79,6 +93,7 @@ describe("Tooltip", () => {
   it("opens tooltip on focus where trigger is non interactive", async () => {
     const user = userEvent.setup();
     render(<NonInteractiveTrigger />);
+    mockFocusVisible(screen.getByText("Just some text").parentElement!);
     expect(screen.queryByRole("tooltip")).toBe(null);
     await user.tab();
     // trigger focused, tooltip shown
@@ -86,6 +101,28 @@ describe("Tooltip", () => {
     screen.getByRole("tooltip");
   });
 
+  it("opens tooltip on long press", async () => {
+    vi.useFakeTimers();
+    try {
+      render(<InteractiveTrigger />);
+      expect(screen.queryByRole("tooltip")).toBe(null);
+      // Press
+      fireEvent.touchStart(screen.getByRole("link"));
+      expect(screen.queryByRole("tooltip")).toBe(null);
+      // And hold
+      await act(() => vi.advanceTimersByTimeAsync(1000));
+      screen.getByRole("tooltip");
+      // And release
+      fireEvent.touchEnd(screen.getByRole("link"));
+      // Tooltip should remain visible for some time
+      screen.getByRole("tooltip");
+      await act(() => vi.advanceTimersByTimeAsync(2000));
+      expect(screen.queryByRole("tooltip")).toBe(null);
+    } finally {
+      vi.useRealTimers();
+    }
+  });
+
   it("overrides default tab index for non interactive triggers", async () => {
     const user = userEvent.setup();
     const Component = composeStory(
diff --git a/src/components/Tooltip/useTooltip.ts b/src/components/Tooltip/useTooltip.ts
index 18367fc1..0a783f93 100644
--- a/src/components/Tooltip/useTooltip.ts
+++ b/src/components/Tooltip/useTooltip.ts
@@ -33,7 +33,14 @@ import {
   useInteractions,
   useRole,
 } from "@floating-ui/react";
-import { useMemo, useRef, useState, JSX, AriaAttributes } from "react";
+import {
+  useMemo,
+  useRef,
+  useState,
+  JSX,
+  AriaAttributes,
+  useEffect,
+} from "react";
 import { hoverDelay } from "./TooltipProvider";
 
 export interface CommonUseTooltipProps {
@@ -168,11 +175,42 @@ export function useTooltip({
     enabled: controlledOpen === undefined,
     // Show tooltip after a delay when trigger is interactive
     delay: isTriggerInteractive ? delay : {},
+    mouseOnly: true,
   });
+
   const focus = useFocus(context, {
     enabled: controlledOpen === undefined,
-    visibleOnly: false,
   });
+
+  // On touch screens, show the tooltip on a long press
+  const pressTimer = useRef<number>();
+  useEffect(() => () => window.clearTimeout(pressTimer.current), []);
+  const press = useMemo(() => {
+    const onTouchEnd = () => {
+      if (pressTimer.current === undefined)
+        pressTimer.current = window.setTimeout(() => {
+          setOpen(false);
+          pressTimer.current = undefined;
+        }, 1500);
+      else window.clearTimeout(pressTimer.current);
+    };
+    return {
+      // Set these props on the anchor element
+      reference: {
+        onTouchStart: () => {
+          if (pressTimer.current !== undefined)
+            window.clearTimeout(pressTimer.current);
+          pressTimer.current = window.setTimeout(() => {
+            setOpen(true);
+            pressTimer.current = undefined;
+          }, 500);
+        },
+        onTouchEnd,
+        onTouchCancel: onTouchEnd,
+      },
+    };
+  }, []);
+
   const dismiss = useDismiss(context);
 
   const purpose = "label" in props ? "label" : "description";
@@ -181,6 +219,7 @@ export function useTooltip({
     enabled: purpose === "description",
     role: "tooltip",
   });
+
   // A label tooltip should set aria-labelledby with no role regardless of
   // whether the tooltip is visible.
   // (Source: https://zoebijl.github.io/apg-tooltip/#tooltip-main-label)
@@ -189,7 +228,7 @@ export function useTooltip({
     () =>
       purpose === "label"
         ? {
-            // The props we want to set on the anchor element
+            // Set these props on the anchor element
             reference: {
               "aria-labelledby": labelId,
               "aria-describedby": caption ? captionId : undefined,
@@ -199,7 +238,14 @@ export function useTooltip({
     [purpose, labelId, captionId],
   );
 
-  const interactions = useInteractions([hover, focus, dismiss, role, label]);
+  const interactions = useInteractions([
+    hover,
+    focus,
+    press,
+    dismiss,
+    role,
+    label,
+  ]);
 
   return useMemo(
     () => ({