diff --git a/utils/generate_types/overrides.d.ts b/utils/generate_types/overrides.d.ts
index 351ccab95387b..69c70f0eb21a3 100644
--- a/utils/generate_types/overrides.d.ts
+++ b/utils/generate_types/overrides.d.ts
@@ -56,14 +56,14 @@ export interface Page {
   $$(selector: string): Promise<HTMLOrSVGElementHandle[]>;
 
   $eval<K extends keyof HTMLElementTagNameMap, R, Arg>(selector: K, pageFunction: PageFunctionOn<HTMLElementTagNameMap[K], Arg, R>, arg: Arg): Promise<R>;
-  $eval<R, Arg>(selector: string, pageFunction: PageFunctionOn<HTMLOrSVGElement, Arg, R>, arg: Arg): Promise<R>;
+  $eval<R, Arg, E extends HTMLOrSVGElement = HTMLOrSVGElement>(selector: string, pageFunction: PageFunctionOn<E, Arg, R>, arg: Arg): Promise<R>;
   $eval<K extends keyof HTMLElementTagNameMap, R>(selector: K, pageFunction: PageFunctionOn<HTMLElementTagNameMap[K], void, R>, arg?: any): Promise<R>;
-  $eval<R>(selector: string, pageFunction: PageFunctionOn<HTMLOrSVGElement, void, R>, arg?: any): Promise<R>;
+  $eval<R, E extends HTMLOrSVGElement = HTMLOrSVGElement>(selector: string, pageFunction: PageFunctionOn<E, void, R>, arg?: any): Promise<R>;
 
   $$eval<K extends keyof HTMLElementTagNameMap, R, Arg>(selector: K, pageFunction: PageFunctionOn<HTMLElementTagNameMap[K][], Arg, R>, arg: Arg): Promise<R>;
-  $$eval<R, Arg>(selector: string, pageFunction: PageFunctionOn<HTMLOrSVGElement[], Arg, R>, arg: Arg): Promise<R>;
+  $$eval<R, Arg, E extends HTMLOrSVGElement = HTMLOrSVGElement>(selector: string, pageFunction: PageFunctionOn<E[], Arg, R>, arg: Arg): Promise<R>;
   $$eval<K extends keyof HTMLElementTagNameMap, R>(selector: K, pageFunction: PageFunctionOn<HTMLElementTagNameMap[K][], void, R>, arg?: any): Promise<R>;
-  $$eval<R>(selector: string, pageFunction: PageFunctionOn<HTMLOrSVGElement[], void, R>, arg?: any): Promise<R>;
+  $$eval<R, E extends HTMLOrSVGElement = HTMLOrSVGElement>(selector: string, pageFunction: PageFunctionOn<E[], void, R>, arg?: any): Promise<R>;
 
   waitForFunction<R, Arg>(pageFunction: PageFunction<Arg, R>, arg: Arg, options?: PageWaitForFunctionOptions): Promise<SmartHandle<R>>;
   waitForFunction<R>(pageFunction: PageFunction<void, R>, arg?: any, options?: PageWaitForFunctionOptions): Promise<SmartHandle<R>>;
@@ -88,14 +88,14 @@ export interface Frame {
   $$(selector: string): Promise<HTMLOrSVGElementHandle[]>;
 
   $eval<K extends keyof HTMLElementTagNameMap, R, Arg>(selector: K, pageFunction: PageFunctionOn<HTMLElementTagNameMap[K], Arg, R>, arg: Arg): Promise<R>;
-  $eval<R, Arg>(selector: string, pageFunction: PageFunctionOn<HTMLOrSVGElement, Arg, R>, arg: Arg): Promise<R>;
+  $eval<R, Arg, E extends HTMLOrSVGElement = HTMLOrSVGElement>(selector: string, pageFunction: PageFunctionOn<E, Arg, R>, arg: Arg): Promise<R>;
   $eval<K extends keyof HTMLElementTagNameMap, R>(selector: K, pageFunction: PageFunctionOn<HTMLElementTagNameMap[K], void, R>, arg?: any): Promise<R>;
-  $eval<R>(selector: string, pageFunction: PageFunctionOn<HTMLOrSVGElement, void, R>, arg?: any): Promise<R>;
+  $eval<R, E extends HTMLOrSVGElement = HTMLOrSVGElement>(selector: string, pageFunction: PageFunctionOn<E, void, R>, arg?: any): Promise<R>;
 
   $$eval<K extends keyof HTMLElementTagNameMap, R, Arg>(selector: K, pageFunction: PageFunctionOn<HTMLElementTagNameMap[K][], Arg, R>, arg: Arg): Promise<R>;
-  $$eval<R, Arg>(selector: string, pageFunction: PageFunctionOn<HTMLOrSVGElement[], Arg, R>, arg: Arg): Promise<R>;
+  $$eval<R, Arg, E extends HTMLOrSVGElement = HTMLOrSVGElement>(selector: string, pageFunction: PageFunctionOn<E[], Arg, R>, arg: Arg): Promise<R>;
   $$eval<K extends keyof HTMLElementTagNameMap, R>(selector: K, pageFunction: PageFunctionOn<HTMLElementTagNameMap[K][], void, R>, arg?: any): Promise<R>;
-  $$eval<R>(selector: string, pageFunction: PageFunctionOn<HTMLOrSVGElement[], void, R>, arg?: any): Promise<R>;
+  $$eval<R, E extends HTMLOrSVGElement = HTMLOrSVGElement>(selector: string, pageFunction: PageFunctionOn<E[], void, R>, arg?: any): Promise<R>;
 
   waitForFunction<R, Arg>(pageFunction: PageFunction<Arg, R>, arg: Arg, options?: PageWaitForFunctionOptions): Promise<SmartHandle<R>>;
   waitForFunction<R>(pageFunction: PageFunction<void, R>, arg?: any, options?: PageWaitForFunctionOptions): Promise<SmartHandle<R>>;
@@ -115,11 +115,11 @@ export interface Worker {
 }
 
 export interface JSHandle<T = any> {
-  evaluate<R, Arg>(pageFunction: PageFunctionOn<T, Arg, R>, arg: Arg): Promise<R>;
-  evaluate<R>(pageFunction: PageFunctionOn<T, void, R>, arg?: any): Promise<R>;
+  evaluate<R, Arg, O extends T = T>(pageFunction: PageFunctionOn<O, Arg, R>, arg: Arg): Promise<R>;
+  evaluate<R, O extends T = T>(pageFunction: PageFunctionOn<O, void, R>, arg?: any): Promise<R>;
 
-  evaluateHandle<R, Arg>(pageFunction: PageFunctionOn<T, Arg, R>, arg: Arg): Promise<SmartHandle<R>>;
-  evaluateHandle<R>(pageFunction: PageFunctionOn<T, void, R>, arg?: any): Promise<SmartHandle<R>>;
+  evaluateHandle<R, Arg, O extends T = T>(pageFunction: PageFunctionOn<O, Arg, R>, arg: Arg): Promise<SmartHandle<R>>;
+  evaluateHandle<R, O extends T = T>(pageFunction: PageFunctionOn<O, void, R>, arg?: any): Promise<SmartHandle<R>>;
 
   jsonValue(): Promise<T>;
   asElement(): T extends Node ? ElementHandle<T> : null;
@@ -133,14 +133,14 @@ export interface ElementHandle<T=Node> extends JSHandle<T> {
   $$(selector: string): Promise<HTMLOrSVGElementHandle[]>;
 
   $eval<K extends keyof HTMLElementTagNameMap, R, Arg>(selector: K, pageFunction: PageFunctionOn<HTMLElementTagNameMap[K], Arg, R>, arg: Arg): Promise<R>;
-  $eval<R, Arg>(selector: string, pageFunction: PageFunctionOn<HTMLOrSVGElement, Arg, R>, arg: Arg): Promise<R>;
+  $eval<R, Arg, E extends HTMLOrSVGElement = HTMLOrSVGElement>(selector: string, pageFunction: PageFunctionOn<E, Arg, R>, arg: Arg): Promise<R>;
   $eval<K extends keyof HTMLElementTagNameMap, R>(selector: K, pageFunction: PageFunctionOn<HTMLElementTagNameMap[K], void, R>, arg?: any): Promise<R>;
-  $eval<R>(selector: string, pageFunction: PageFunctionOn<HTMLOrSVGElement, void, R>, arg?: any): Promise<R>;
+  $eval<R, E extends HTMLOrSVGElement = HTMLOrSVGElement>(selector: string, pageFunction: PageFunctionOn<E, void, R>, arg?: any): Promise<R>;
 
   $$eval<K extends keyof HTMLElementTagNameMap, R, Arg>(selector: K, pageFunction: PageFunctionOn<HTMLElementTagNameMap[K][], Arg, R>, arg: Arg): Promise<R>;
-  $$eval<R, Arg>(selector: string, pageFunction: PageFunctionOn<HTMLOrSVGElement[], Arg, R>, arg: Arg): Promise<R>;
+  $$eval<R, Arg, E extends HTMLOrSVGElement = HTMLOrSVGElement>(selector: string, pageFunction: PageFunctionOn<E[], Arg, R>, arg: Arg): Promise<R>;
   $$eval<K extends keyof HTMLElementTagNameMap, R>(selector: K, pageFunction: PageFunctionOn<HTMLElementTagNameMap[K][], void, R>, arg?: any): Promise<R>;
-  $$eval<R>(selector: string, pageFunction: PageFunctionOn<HTMLOrSVGElement[], void, R>, arg?: any): Promise<R>;
+  $$eval<R, E extends HTMLOrSVGElement = HTMLOrSVGElement>(selector: string, pageFunction: PageFunctionOn<E[], void, R>, arg?: any): Promise<R>;
 }
 
 export interface BrowserType<Browser> {
diff --git a/utils/generate_types/test/test.ts b/utils/generate_types/test/test.ts
index 3591ae912d5ac..ca9867c89c983 100644
--- a/utils/generate_types/test/test.ts
+++ b/utils/generate_types/test/test.ts
@@ -286,13 +286,57 @@ playwright.chromium.launch().then(async browser => {
     console.log(elements.map(x => x)[0].textContent);
     return elements[3].innerHTML;
   });
-  {
-    const value = await page.$eval('input', i => i.disabled);
-    const assertion: AssertType<boolean, typeof value> = true;
-  }
-  {
-    const value = await page.$$eval('input', i => i[0].defaultValue);
-    const assertion: AssertType<string, typeof value> = true;
+  const frame = page.frames()[0];
+  const handle = await page.evaluateHandle(() => document.body);
+  for (const object of [frame, handle, page]) {
+    {
+      const value = await object.$eval('*[foo=bar]', i => i.textContent);
+      const assertion: AssertType<string, typeof value> = true;
+    }
+    {
+      const value = await object.$eval('input', i => i.disabled);
+      const assertion: AssertType<boolean, typeof value> = true;
+    }
+    {
+      const value = await object.$eval('input[foo=bar]', (i: HTMLInputElement) => i.disabled);
+      const assertion: AssertType<boolean, typeof value> = true;
+    }
+    {
+      const value = await object.$eval('*[foo=bar]', (i, dummy) => i.textContent, 2);
+      const assertion: AssertType<string, typeof value> = true;
+    }
+    {
+      const value = await object.$eval('input', (i, dummy) => i.disabled, 2);
+      const assertion: AssertType<boolean, typeof value> = true;
+    }
+    {
+      const value = await object.$eval('input[foo=bar]', (i: HTMLInputElement, dummy: number) => i.disabled, 2);
+      const assertion: AssertType<boolean, typeof value> = true;
+    }
+    {
+      const value = await object.$$eval('*[foo=bar]', i => i[0].textContent);
+      const assertion: AssertType<string, typeof value> = true;
+    }
+    {
+      const value = await object.$$eval('input', i => i[0].defaultValue);
+      const assertion: AssertType<string, typeof value> = true;
+    }
+    {
+      const value = await object.$$eval('input[foo=bar]', (i: HTMLInputElement[]) => i[0].defaultValue);
+      const assertion: AssertType<string, typeof value> = true;
+    }
+    {
+      const value = await object.$$eval('*[foo=bar]', (i, dummy) => i[0].textContent, 2);
+      const assertion: AssertType<string, typeof value> = true;
+    }
+    {
+      const value = await object.$$eval('input', (i, dummy) => i[0].defaultValue, 2);
+      const assertion: AssertType<string, typeof value> = true;
+    }
+    {
+      const value = await object.$$eval('input[foo=bar]', (i: HTMLInputElement[], dummy: number) => i[0].defaultValue, 2);
+      const assertion: AssertType<string, typeof value> = true;
+    }
   }
   browser.close();
 })();
@@ -343,7 +387,69 @@ playwright.chromium.launch().then(async browser => {
     const value = await windowHandle.evaluate((x: Window, b) => b, 'world');
     const assertion: AssertType<string, typeof value> = true;
   }
+  {
+    const value = await page.evaluate(({a, b}) => b ? a : '123', { a: 3, b: true });
+    const assertion: AssertType<number | string, typeof value> = true;
+  }
+  {
+    const value = await page.evaluate(([a, b, c]) => ({a, b, c}), [3, '123', true]);
+    const assertion: AssertType<{a: string | number | boolean, b: string | number | boolean, c: string | number | boolean}, typeof value> = true;
+  }
+  {
+    const value = await page.evaluate(([a, b, c]) => ({a, b, c}), [3, '123', true] as const);
+    const assertion: AssertType<{a: 3, b: '123', c: true}, typeof value> = true;
+  }
 
+  {
+    const handle = await page.evaluateHandle(() => ([{a: '123'}]));
+    const value = await handle.evaluate(h => h[1].a);
+    const assertion: AssertType<string, typeof value> = true;
+  }
+  {
+    const handle = await page.evaluateHandle(() => ([{a: '123'}]));
+    const value = await handle.evaluate((h, p) => ({ a: h[1].a, p}), 123);
+    const assertion: AssertType<{a: string, p: number}, typeof value> = true;
+  }
+  {
+    const handle = await page.evaluateHandle(() => ([{a: '123'}]));
+    const value = await handle.evaluate((h: ({a: string, b: number})[]) => h[1].b);
+    const assertion: AssertType<number, typeof value> = true;
+  }
+  {
+    const handle = await page.evaluateHandle(() => ([{a: '123'}]));
+    const value = await handle.evaluate((h: ({a: string, b: number})[], prop) => h[1][prop], 'b' as const);
+    const assertion: AssertType<number, typeof value> = true;
+  }
+  {
+    const handle = await page.evaluateHandle(() => ([{a: '123'}]));
+    const value = await handle.evaluateHandle(h => h[1].a);
+    const assertion: AssertType<playwright.JSHandle<string>, typeof value> = true;
+  }
+  {
+    const handle = await page.evaluateHandle(() => ([{a: '123'}]));
+    const value = await handle.evaluateHandle((h, p) => ({ a: h[1].a, p}), 123);
+    const assertion: AssertType<playwright.JSHandle<{a: string, p: number}>, typeof value> = true;
+  }
+  {
+    const handle = await page.evaluateHandle(() => ([{a: '123'}]));
+    const value = await handle.evaluateHandle((h: ({a: string, b: number})[]) => h[1].b);
+    const assertion: AssertType<playwright.JSHandle<number>, typeof value> = true;
+  }
+  {
+    const handle = await page.waitForSelector('*');
+    const value = await handle.evaluate((e: HTMLInputElement) => e.disabled);
+    const assertion: AssertType<boolean, typeof value> = true;
+  }
+  {
+    const handle = await page.waitForSelector('*');
+    const value = await handle.evaluate((e: HTMLInputElement, x) => e.disabled || x, 123);
+    const assertion: AssertType<boolean | number, typeof value> = true;
+  }
+  {
+    const handle = await page.waitForSelector('*');
+    const value = await handle.evaluateHandle((e: HTMLInputElement, x) => e.disabled || x, 123);
+    const assertion: AssertType<playwright.JSHandle<boolean> | playwright.JSHandle<number>, typeof value> = true;
+  }
 
   {
     const handle = await page.evaluateHandle(() => 'hello');