diff --git a/types/expect-puppeteer/index.d.ts b/types/expect-puppeteer/index.d.ts
index b77bc948bd47d7..018e342ce8588b 100644
--- a/types/expect-puppeteer/index.d.ts
+++ b/types/expect-puppeteer/index.d.ts
@@ -3,7 +3,7 @@
 // Definitions by: Josh Goldberg <https://github.com/JoshuaKGoldberg>
 //                 Tanguy Krotoff <https://github.com/tkrotoff>
 // Definitions: https://github.com/DefinitelyTyped/DefinitelyTyped
-// TypeScript Version: 2.8
+// TypeScript Version: 3.0
 
 /// <reference types="jest" />
 
diff --git a/types/jest-axe/index.d.ts b/types/jest-axe/index.d.ts
index 60375e3605cc85..506236773f57da 100644
--- a/types/jest-axe/index.d.ts
+++ b/types/jest-axe/index.d.ts
@@ -2,7 +2,7 @@
 // Project: https://github.com/nickcolley/jest-axe
 // Definitions by: Josh Goldberg <https://github.com/JoshuaKGoldberg>
 // Definitions: https://github.com/DefinitelyTyped/DefinitelyTyped
-// TypeScript Version: 2.4
+// TypeScript Version: 3.0
 
 /// <reference types="jest" />
 
diff --git a/types/jest-image-snapshot/index.d.ts b/types/jest-image-snapshot/index.d.ts
index c15e435cc96116..8eeff209903adc 100644
--- a/types/jest-image-snapshot/index.d.ts
+++ b/types/jest-image-snapshot/index.d.ts
@@ -2,7 +2,7 @@
 // Project: https://github.com/americanexpress/jest-image-snapshot#readme
 // Definitions by: Janeene Beeforth <https://github.com/dawnmist>
 // Definitions: https://github.com/DefinitelyTyped/DefinitelyTyped
-// TypeScript Version: 2.3
+// TypeScript Version: 3.0
 
 /// <reference types="jest" />
 
diff --git a/types/jest-in-case/index.d.ts b/types/jest-in-case/index.d.ts
index 02d7d08af94d52..9762bc39d3ba6d 100644
--- a/types/jest-in-case/index.d.ts
+++ b/types/jest-in-case/index.d.ts
@@ -2,7 +2,7 @@
 // Project: https://github.com/thinkmill/jest-in-case#readme
 // Definitions by: Geovani de Souza <https://github.com/geovanisouza92>
 // Definitions: https://github.com/DefinitelyTyped/DefinitelyTyped
-// TypeScript Version: 2.3
+// TypeScript Version: 3.0
 
 /// <reference types="jest" />
 /// <reference types="node" />
diff --git a/types/jest-in-case/jest-in-case-tests.ts b/types/jest-in-case/jest-in-case-tests.ts
index 283ade76c134c1..6af60a5fd42731 100644
--- a/types/jest-in-case/jest-in-case-tests.ts
+++ b/types/jest-in-case/jest-in-case-tests.ts
@@ -11,8 +11,8 @@ function subtract(minuend: number, subtrahend: number) {
 }
 
 beforeEach(() => {
-    jest.spyOn(global, 'describe').mockImplementation((title, fn) => fn());
-    jest.spyOn(global, 'test').mockImplementation((name, fn) => fn());
+    jest.spyOn(global, 'describe').mockImplementation((title, fn) => jest.fn());
+    jest.spyOn(global, 'test').mockImplementation((name, fn) => jest.fn());
     global.test.skip = jest.fn((name, fn) => fn());
     global.test.only = jest.fn((name, fn) => fn());
 });
@@ -54,8 +54,8 @@ test('array', () => {
 });
 
 test('object', () => {
-    jest.spyOn(global, 'describe').mockImplementation((title, fn) => fn());
-    jest.spyOn(global, 'test').mockImplementation((name, fn) => fn());
+    jest.spyOn(global, 'describe').mockImplementation((title, fn) => jest.fn());
+    jest.spyOn(global, 'test').mockImplementation((name, fn) => jest.fn());
 
     const title = 'add(augend, addend)';
 
diff --git a/types/jest-json-schema/index.d.ts b/types/jest-json-schema/index.d.ts
index 67f1c51f7e0803..b2133526dc2d78 100644
--- a/types/jest-json-schema/index.d.ts
+++ b/types/jest-json-schema/index.d.ts
@@ -2,7 +2,7 @@
 // Project: https://github.com/americanexpress/jest-json-schema#readme
 // Definitions by: Igor Korolev <https://github.com/deadNightTiger>
 // Definitions: https://github.com/DefinitelyTyped/DefinitelyTyped
-// TypeScript Version: 2.3
+// TypeScript Version: 3.0
 
 /// <reference types="jest" />
 import * as ajv from "ajv";
diff --git a/types/jest-matchers/index.d.ts b/types/jest-matchers/index.d.ts
index 3b028f8929f26f..705f993ea3b256 100644
--- a/types/jest-matchers/index.d.ts
+++ b/types/jest-matchers/index.d.ts
@@ -2,7 +2,7 @@
 // Project: https://github.com/facebook/jest#readme
 // Definitions by: Joscha Feth <https://github.com/joscha>
 // Definitions: https://github.com/DefinitelyTyped/DefinitelyTyped
-// TypeScript Version: 2.3
+// TypeScript Version: 3.0
 
 /// <reference types="jest" />
 export = expect;
diff --git a/types/jest-plugin-context/index.d.ts b/types/jest-plugin-context/index.d.ts
index da2698b78e6ae7..814b334b12108f 100644
--- a/types/jest-plugin-context/index.d.ts
+++ b/types/jest-plugin-context/index.d.ts
@@ -2,7 +2,7 @@
 // Project: https://github.com/negativetwelve/jest-plugins/tree/master/packages/jest-plugin-context
 // Definitions by: Jonas Heinrich <https://github.com/jonasheinrich>
 // Definitions: https://github.com/DefinitelyTyped/DefinitelyTyped
-// TypeScript Version: 2.3
+// TypeScript Version: 3.0
 
 /// <reference types="jest" />
 
diff --git a/types/jest-specific-snapshot/index.d.ts b/types/jest-specific-snapshot/index.d.ts
index 61a65a416a9d4d..0e0a43d895ed8a 100644
--- a/types/jest-specific-snapshot/index.d.ts
+++ b/types/jest-specific-snapshot/index.d.ts
@@ -2,7 +2,7 @@
 // Project: https://github.com/igor-dv/jest-specific-snapshot#readme
 // Definitions by: Janeene Beeforth <https://github.com/dawnmist>
 // Definitions: https://github.com/DefinitelyTyped/DefinitelyTyped
-// TypeScript Version: 2.8
+// TypeScript Version: 3.0
 
 /// <reference types="jest" />
 
diff --git a/types/jest-when/index.d.ts b/types/jest-when/index.d.ts
index f484502f4d9284..c76fdd1a9bd72a 100644
--- a/types/jest-when/index.d.ts
+++ b/types/jest-when/index.d.ts
@@ -2,26 +2,17 @@
 // Project: https://github.com/timkindberg/jest-when#readme
 // Definitions by: Alden Taylor <https://github.com/aldentaylor>
 // Definitions: https://github.com/DefinitelyTyped/DefinitelyTyped
-// TypeScript Version: 2.3
+// TypeScript Version: 3.0
 
 /// <reference types="jest" />
 
-export interface PartialMockInstance<T> {
-  mockReturnValue: jest.MockInstance<T>['mockReturnValue'];
-  mockReturnValueOnce: jest.MockInstance<T>['mockReturnValueOnce'];
-  mockResolvedValue: jest.MockInstance<T>['mockResolvedValue'];
-  mockResolvedValueOnce: jest.MockInstance<T>['mockResolvedValueOnce'];
-  mockRejectedValue: jest.MockInstance<T>['mockRejectedValue'];
-  mockRejectedValueOnce: jest.MockInstance<T>['mockRejectedValueOnce'];
-}
+export type PartialMockInstance<T, Y extends any[]> = Pick<jest.MockInstance<T, Y>, 'mockReturnValue' | 'mockReturnValueOnce' | 'mockResolvedValue'
+  | 'mockResolvedValueOnce' | 'mockRejectedValue' | 'mockRejectedValueOnce'>;
 
-export interface When {
-  <T>(fn: jest.Mocked<T> | jest.Mock<T>): When;
-  // due to no-unnecessary-generics lint rule, the generics have been replaced with 'any'
-  // calledWith<T>(...matchers: any[]): PartialMockInstance<T>;
-  // expectCalledWith<T>(...matchers: any[]): PartialMockInstance<T>;
-  calledWith(...matchers: any[]): PartialMockInstance<any>;
-  expectCalledWith(...matchers: any[]): PartialMockInstance<any>;
+export interface When<T = {}, Y extends any[] = any> {
+  (fn: jest.Mock<T, Y>): When<T, Y>;
+  calledWith(...matchers: Y): PartialMockInstance<T, Y>;
+  expectCalledWith(...matchers: Y): PartialMockInstance<T, Y>;
 }
 
 export const when: When;
diff --git a/types/jest-when/jest-when-tests.ts b/types/jest-when/jest-when-tests.ts
index 13da65928dfd3b..70e0041341de19 100644
--- a/types/jest-when/jest-when-tests.ts
+++ b/types/jest-when/jest-when-tests.ts
@@ -31,16 +31,20 @@ describe('mock-when test', () => {
 
   it('Supports compound declarations:', () => {
     const fn = jest.fn();
-    when(fn).calledWith(1).mockReturnValue('no');
+    when(fn).calledWith(1).mockReturnValueOnce('no').mockReturnValue('yes');
     when(fn).calledWith(2).mockReturnValue('way?');
-    when(fn).calledWith(3).mockReturnValue('yes');
-    when(fn).calledWith(4).mockReturnValue('way!');
+    when(fn).calledWith(3).mockResolvedValueOnce('no');
+    when(fn).calledWith(3).mockResolvedValue('yes');
+    when(fn).calledWith(4).mockRejectedValueOnce('no');
+    when(fn).calledWith(4).mockRejectedValue('yes');
 
     expect(fn(1)).toEqual('no');
+    expect(fn(1)).toEqual('yes');
     expect(fn(2)).toEqual('way?');
-    expect(fn(3)).toEqual('yes');
-    expect(fn(4)).toEqual('way!');
-    expect(fn(5)).toEqual(undefined);
+    expect(fn(3)).resolves.toEqual('no');
+    expect(fn(3)).resolves.toEqual('yes');
+    expect(fn(4)).rejects.toEqual('no');
+    expect(fn(4)).rejects.toEqual('yes');
   });
 
   it('Assert the args:', () => {
diff --git a/types/jest/index.d.ts b/types/jest/index.d.ts
index d434b5e1988a67..89979493b74ac7 100644
--- a/types/jest/index.d.ts
+++ b/types/jest/index.d.ts
@@ -17,8 +17,9 @@
 //                 Martin Hochel <https://github.com/hotell>
 //                 Sebastian Sebald <https://github.com/sebald>
 //                 Andy <https://github.com/andys8>
+//                 Antoine Brault <https://github.com/antoinebrault>
 // Definitions: https://github.com/DefinitelyTyped/DefinitelyTyped
-// TypeScript Version: 2.3
+// TypeScript Version: 3.0
 
 declare var beforeAll: jest.Lifecycle;
 declare var beforeEach: jest.Lifecycle;
@@ -35,6 +36,8 @@ declare var xtest: jest.It;
 
 declare const expect: jest.Expect;
 
+type ArgsType<T> = T extends (...args: infer A) => any ? A : never;
+
 interface NodeRequire {
     /**
      * Returns the actual module instead of a mock, bypassing all checks on
@@ -110,11 +113,7 @@ declare namespace jest {
     /**
      * Creates a mock function. Optionally takes a mock implementation.
      */
-    function fn<T extends {}>(implementation: (...args: any[]) => T): Mock<T>;
-    /**
-     * Creates a mock function. Optionally takes a mock implementation.
-     */
-    function fn<T>(implementation?: (...args: any[]) => any): Mock<T>;
+    function fn<T, Y extends any[]>(implementation?: (...args: Y) => T): Mock<T, Y>;
     /**
      * Use the automatic mocking system to generate a mocked version of the given module.
      */
@@ -122,7 +121,7 @@ declare namespace jest {
     /**
      * Returns whether the given function is a mock function.
      */
-    function isMockFunction(fn: any): fn is Mock<any>;
+    function isMockFunction(fn: any): fn is Mock;
     /**
      * Mocks a module with an auto-mocked version when it is being required.
      */
@@ -198,7 +197,9 @@ declare namespace jest {
      *   spy.mockRestore();
      * });
      */
-    function spyOn<T extends {}, M extends keyof T>(object: T, method: M, accessType?: 'get' | 'set'): SpyInstance<T[M]>;
+    function spyOn<T extends {}, M extends keyof T>(object: T, method: M, accessType: 'get'): SpyInstance<T[M], []>;
+    function spyOn<T extends {}, M extends keyof T>(object: T, method: M, accessType: 'set'): SpyInstance<void, [T[M]]>;
+    function spyOn<T extends {}, M extends keyof T>(object: T, method: M): T[M] extends (...args: any[]) => any ? SpyInstance<ReturnType<T[M]>, ArgsType<T[M]>> : never;
     /**
      * Indicates that the module system should never return a mocked version of
      * the specified module from require() (e.g. that it should always return the real module).
@@ -762,12 +763,12 @@ declare namespace jest {
         new (...args: any[]): any;
     }
 
-    interface Mock<T = {}> extends Function, MockInstance<T> {
-        new (...args: any[]): T;
-        (...args: any[]): any;
+    interface Mock<T = any, Y extends any[] = any> extends Function, MockInstance<T, Y> {
+        new (...args: Y): T;
+        (...args: Y): T;
     }
 
-    interface SpyInstance<T = {}> extends MockInstance<T> {}
+    interface SpyInstance<T = any, Y extends any[] = any> extends MockInstance<T, Y> {}
 
     /**
      * Wrap module with mock definitions
@@ -781,14 +782,14 @@ declare namespace jest {
      *  myApi.myApiMethod.mockImplementation(() => "test");
      */
     type Mocked<T> = {
-        [P in keyof T]: T[P] & MockInstance<T[P]>;
+        [P in keyof T]: T[P] & MockInstance<T[P], ArgsType<T[P]>>;
     } & T;
 
-    interface MockInstance<T> {
+    interface MockInstance<T, Y extends any[]> {
         /** Returns the mock name string set by calling `mockFn.mockName(value)`. */
         getMockName(): string;
         /** Provides access to the mock's metadata */
-        mock: MockContext<T>;
+        mock: MockContext<T, Y>;
         /**
          * Resets all information stored in the mockFn.mock.calls and mockFn.mock.instances arrays.
          *
@@ -828,7 +829,7 @@ declare namespace jest {
          *
          * Note: `jest.fn(implementation)` is a shorthand for `jest.fn().mockImplementation(implementation)`.
          */
-        mockImplementation(fn?: (...args: any[]) => any): Mock<T>;
+        mockImplementation(fn?: (...args: Y) => T): Mock<T, Y>;
         /**
          * Accepts a function that will be used as an implementation of the mock for one call to the mocked function.
          * Can be chained so that multiple function calls produce different results.
@@ -844,9 +845,9 @@ declare namespace jest {
          *
          * myMockFn((err, val) => console.log(val)); // false
          */
-        mockImplementationOnce(fn: (...args: any[]) => any): Mock<T>;
+        mockImplementationOnce(fn: (...args: Y) => T): Mock<T, Y>;
         /** Sets the name of the mock`. */
-        mockName(name: string): Mock<T>;
+        mockName(name: string): Mock<T, Y>;
         /**
          * Just a simple sugar function for:
          *
@@ -856,7 +857,7 @@ declare namespace jest {
          *     return this;
          *   });
          */
-        mockReturnThis(): Mock<T>;
+        mockReturnThis(): Mock<T, Y>;
         /**
          * Accepts a value that will be returned whenever the mock function is called.
          *
@@ -868,7 +869,7 @@ declare namespace jest {
          * mock.mockReturnValue(43);
          * mock(); // 43
          */
-        mockReturnValue(value: any): Mock<T>;
+        mockReturnValue(value: T): Mock<T, Y>;
         /**
          * Accepts a value that will be returned for one call to the mock function. Can be chained so that
          * successive calls to the mock function return different values. When there are no more
@@ -885,11 +886,11 @@ declare namespace jest {
          * console.log(myMockFn(), myMockFn(), myMockFn(), myMockFn());
          *
          */
-        mockReturnValueOnce(value: any): Mock<T>;
+        mockReturnValueOnce(value: T): Mock<T, Y>;
         /**
          * Simple sugar function for: `jest.fn().mockImplementation(() => Promise.resolve(value));`
          */
-        mockResolvedValue(value: any): Mock<T>;
+        mockResolvedValue(value: T | PromiseLike<T>): Mock<Promise<T>, Y>;
         /**
          * Simple sugar function for: `jest.fn().mockImplementationOnce(() => Promise.resolve(value));`
          *
@@ -909,7 +910,7 @@ declare namespace jest {
          * });
          *
          */
-        mockResolvedValueOnce(value: any): Mock<T>;
+        mockResolvedValueOnce(value: T | PromiseLike<T>): Mock<Promise<T>, Y>;
         /**
          * Simple sugar function for: `jest.fn().mockImplementation(() => Promise.reject(value));`
          *
@@ -921,7 +922,7 @@ declare namespace jest {
          *   await asyncMock(); // throws "Async error"
          * });
          */
-        mockRejectedValue(value: any): Mock<T>;
+        mockRejectedValue(value: any): Mock<Promise<T>, Y>;
 
         /**
          * Simple sugar function for: `jest.fn().mockImplementationOnce(() => Promise.reject(value));`
@@ -939,7 +940,7 @@ declare namespace jest {
          * });
          *
          */
-        mockRejectedValueOnce(value: any): Mock<T>;
+        mockRejectedValueOnce(value: any): Mock<Promise<T>, Y>;
     }
 
     /**
@@ -957,8 +958,8 @@ declare namespace jest {
         value: any;
     }
 
-    interface MockContext<T> {
-        calls: any[][];
+    interface MockContext<T, Y extends any[]> {
+        calls: Y[];
         instances: T[];
         invocationCallOrder: number[];
         /**
diff --git a/types/jest/jest-tests.ts b/types/jest/jest-tests.ts
index de1ba904569322..0b7b2c21d99446 100644
--- a/types/jest/jest-tests.ts
+++ b/types/jest/jest-tests.ts
@@ -253,12 +253,34 @@ jest
 
 /* Mocks and spies */
 
-const mock1: jest.Mock = jest.fn();
-const mock2: jest.Mock<undefined> = jest.fn<undefined>(() => undefined);
-const mock3: jest.Mock<string> = jest.fn(() => "abc");
-const mock4: jest.Mock<"abc"> = jest.fn((): "abc" => "abc");
-const mock5: jest.Mock<string> = jest.fn((...args: string[]) => args.join(""));
-const mock6: jest.Mock = jest.fn((arg: {}) => arg);
+// $ExpectType Mock<{}, any[]>
+const mock1 = jest.fn();
+// $ExpectType Mock<undefined, []>
+const mock2 = jest.fn(() => undefined);
+// $ExpectType Mock<string, []>
+const mock3 = jest.fn(() => "abc");
+// $ExpectType Mock<"abc", []>
+const mock4 = jest.fn((): "abc" => "abc");
+// $ExpectType Mock<string, string[]>
+const mock5 = jest.fn((...args: string[]) => args.join(""));
+// $ExpectType Mock<{}, [{}]>
+const mock6 = jest.fn((arg: {}) => arg);
+// $ExpectType Mock<number, [number]>
+const mock7 = jest.fn((arg: number) => arg);
+// $ExpectType Mock<number, [number]>
+const mock8: jest.Mock = jest.fn((arg: number) => arg);
+
+// $ExpectError
+mock7('abc');
+// $ExpectError
+mock7.mockImplementation((arg: string) => 1);
+// compiles because mock8 is declared as jest.Mock<{}, any>
+mock8('abc');
+mock8.mockImplementation((arg: string) => 1);
+
+const mock9 = jest.fn((a: number, _b: string, _c: {}, _iReallyDontCare: [], _makeItStop: boolean) => Promise.resolve(_makeItStop));
+// mockImplementation not required to declare all arguments
+mock9.mockImplementation((a: number) => Promise.resolve(a === 0));
 
 const genMockModule1: {} = jest.genMockFromModule("moduleName");
 const genMockModule2: { a: "b" } = jest.genMockFromModule<{ a: "b" }>("moduleName");
@@ -272,8 +294,8 @@ if (jest.isMockFunction(maybeMock)) {
 }
 
 const mockName: string = jest.fn().getMockName();
-const mockContextVoid: jest.MockContext<void> = jest.fn<void>().mock;
-const mockContextString: jest.MockContext<string> = jest.fn(() => "").mock;
+const mockContextVoid = jest.fn().mock;
+const mockContextString = jest.fn(() => "").mock;
 
 jest.fn().mockClear();
 
@@ -283,14 +305,28 @@ jest.fn().mockRestore();
 
 const spiedTarget = {
     returnsVoid(): void { },
+    setValue(value: string): void {
+        this.value = value;
+    },
     returnsString(): string {
         return "";
     }
 };
 
+class SpiedTargetClass {
+    private _value = 3;
+    get value() {
+        return this._value;
+    }
+    set value(value) {
+        this._value = value;
+    }
+}
+const spiedTarget2 = new SpiedTargetClass();
+
 const spy1 = jest.spyOn(spiedTarget, "returnsVoid");
 const spy2 = jest.spyOn(spiedTarget, "returnsVoid", "get");
-const spy3 = jest.spyOn(spiedTarget, "returnsString", "set");
+const spy3 = jest.spyOn(spiedTarget, "returnsString");
 const spy1Name: string = spy1.getMockName();
 
 const spy2Calls: any[][] = spy2.mock.calls;
@@ -298,9 +334,10 @@ const spy2Calls: any[][] = spy2.mock.calls;
 spy2.mockClear();
 spy2.mockReset();
 
-const spy3Mock: jest.Mock<() => string> = spy3
+const spy3Mock = spy3
     .mockImplementation(() => "")
     .mockImplementation()
+    // $ExpectError
     .mockImplementation((arg: {}) => arg)
     .mockImplementation((...args: string[]) => args.join(""))
     .mockImplementationOnce(() => "")
@@ -314,10 +351,22 @@ const spy3Mock: jest.Mock<() => string> = spy3
     .mockRejectedValueOnce("value");
 
 let spy4: jest.SpyInstance;
-
 spy4 = jest.spyOn(spiedTarget, "returnsString");
+// compiles because spy4 is declared as jest.SpyInstance<{}, any>
+spy4.mockImplementation(() => 1);
 spy4.mockRestore();
 
+// $ExpectType SpyInstance<number, []>
+const spy5 = jest.spyOn(spiedTarget2, "value", "get");
+// $ExpectError
+spy5.mockReturnValue('5');
+
+// $ExpectType SpyInstance<void, [number]>
+const spy6 = jest.spyOn(spiedTarget2, "value", "set");
+
+let spy7: jest.SpyInstance;
+spy7 = jest.spyOn(spiedTarget, "setValue");
+
 /* Snapshot serialization */
 
 const snapshotSerializerPlugin: jest.SnapshotSerializerPlugin = {
diff --git a/types/jest/tsconfig.json b/types/jest/tsconfig.json
index 8a020048400ca5..20bc02a53b5c2d 100644
--- a/types/jest/tsconfig.json
+++ b/types/jest/tsconfig.json
@@ -13,6 +13,7 @@
         "typeRoots": [
             "../"
         ],
+        "target": "es5",
         "types": [],
         "noEmit": true,
         "forceConsistentCasingInFileNames": true
diff --git a/types/storybook__addon-storyshots/index.d.ts b/types/storybook__addon-storyshots/index.d.ts
index dc1a2c59532bc8..9b0517cb9fc710 100644
--- a/types/storybook__addon-storyshots/index.d.ts
+++ b/types/storybook__addon-storyshots/index.d.ts
@@ -2,7 +2,7 @@
 // Project: https://github.com/storybooks/storybook/tree/master/addons/storyshots
 // Definitions by: Bradley Ayers <https://github.com/bradleyayers>
 // Definitions: https://github.com/DefinitelyTyped/DefinitelyTyped
-// TypeScript Version: 2.8
+// TypeScript Version: 3.0
 
 import * as React from 'react';
 import { StoryObject } from '@storybook/react';