diff --git a/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap b/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap
index 9ad0022d6ade..30279159d8fc 100644
--- a/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap
+++ b/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap
@@ -1954,6 +1954,35 @@ Received:
   <red>[1, 2, 3]</>"
 `;
 
+exports[`.toEqual() {pass: false} expect([1, 2]).not.toEqual([1, 2]) 1`] = `
+"<dim>expect(<red>received</><dim>).not.toEqual(<green>expected</><dim>)
+
+Expected value to not equal:
+  <green>[1, 2]</>
+Received:
+  <red>[1, 2]</>"
+`;
+
+exports[`.toEqual() {pass: false} expect([1, 2]).toEqual([2, 1]) 1`] = `
+"<dim>expect(<red>received</><dim>).toEqual(<green>expected</><dim>)
+
+Expected value to equal:
+  <green>[2, 1]</>
+Received:
+  <red>[1, 2]</>
+
+Difference:
+
+<green>- Expected</>
+<red>+ Received</>
+
+<dim>  Array [
+<red>+   1,</>
+<dim>    2,
+<green>-   1,</>
+<dim>  ]"
+`;
+
 exports[`.toEqual() {pass: false} expect([1, 3]).toEqual(ArrayContaining [1, 2]) 1`] = `
 "<dim>expect(<red>received</><dim>).toEqual(<green>expected</><dim>)
 
@@ -1975,6 +2004,34 @@ Difference:
 <dim>  ]"
 `;
 
+exports[`.toEqual() {pass: false} expect([1]).not.toEqual([1]) 1`] = `
+"<dim>expect(<red>received</><dim>).not.toEqual(<green>expected</><dim>)
+
+Expected value to not equal:
+  <green>[1]</>
+Received:
+  <red>[1]</>"
+`;
+
+exports[`.toEqual() {pass: false} expect([1]).toEqual([2]) 1`] = `
+"<dim>expect(<red>received</><dim>).toEqual(<green>expected</><dim>)
+
+Expected value to equal:
+  <green>[2]</>
+Received:
+  <red>[1]</>
+
+Difference:
+
+<green>- Expected</>
+<red>+ Received</>
+
+<dim>  Array [
+<green>-   2,</>
+<red>+   1,</>
+<dim>  ]"
+`;
+
 exports[`.toEqual() {pass: false} expect([Function anonymous]).not.toEqual(Any<Function>) 1`] = `
 "<dim>expect(<red>received</><dim>).not.toEqual(<green>expected</><dim>)
 
@@ -2051,6 +2108,15 @@ Received:
   <red>{\\"a\\": 99}</>"
 `;
 
+exports[`.toEqual() {pass: false} expect({}).not.toEqual({}) 1`] = `
+"<dim>expect(<red>received</><dim>).not.toEqual(<green>expected</><dim>)
+
+Expected value to not equal:
+  <green>{}</>
+Received:
+  <red>{}</>"
+`;
+
 exports[`.toEqual() {pass: false} expect(0).toEqual(-0) 1`] = `
 "<dim>expect(<red>received</><dim>).toEqual(<green>expected</><dim>)
 
@@ -2095,6 +2161,66 @@ Difference:
   Comparing two different types of values. Expected <green>array</> but received <red>number</>."
 `;
 
+exports[`.toEqual() {pass: false} expect(Map {"a" => 0}).toEqual(Map {"b" => 0}) 1`] = `
+"<dim>expect(<red>received</><dim>).toEqual(<green>expected</><dim>)
+
+Expected value to equal:
+  <green>Map {\\"b\\" => 0}</>
+Received:
+  <red>Map {\\"a\\" => 0}</>
+
+Difference:
+
+<green>- Expected</>
+<red>+ Received</>
+
+<dim>  Map {
+<green>-   \\"b\\" => 0,</>
+<red>+   \\"a\\" => 0,</>
+<dim>  }"
+`;
+
+exports[`.toEqual() {pass: false} expect(Map {"v" => 1}).toEqual(Map {"v" => 2}) 1`] = `
+"<dim>expect(<red>received</><dim>).toEqual(<green>expected</><dim>)
+
+Expected value to equal:
+  <green>Map {\\"v\\" => 2}</>
+Received:
+  <red>Map {\\"v\\" => 1}</>
+
+Difference:
+
+<green>- Expected</>
+<red>+ Received</>
+
+<dim>  Map {
+<green>-   \\"v\\" => 2,</>
+<red>+   \\"v\\" => 1,</>
+<dim>  }"
+`;
+
+exports[`.toEqual() {pass: false} expect(Map {}).not.toEqual(Map {}) 1`] = `
+"<dim>expect(<red>received</><dim>).not.toEqual(<green>expected</><dim>)
+
+Expected value to not equal:
+  <green>Map {}</>
+Received:
+  <red>Map {}</>"
+`;
+
+exports[`.toEqual() {pass: false} expect(Map {}).toEqual(Set {}) 1`] = `
+"<dim>expect(<red>received</><dim>).toEqual(<green>expected</><dim>)
+
+Expected value to equal:
+  <green>Set {}</>
+Received:
+  <red>Map {}</>
+
+Difference:
+
+  Comparing two different types of values. Expected <green>set</> but received <red>map</>."
+`;
+
 exports[`.toEqual() {pass: false} expect(Map {1 => "one", 2 => "two"}).not.toEqual(Map {1 => "one", 2 => "two"}) 1`] = `
 "<dim>expect(<red>received</><dim>).not.toEqual(<green>expected</><dim>)
 
@@ -2132,6 +2258,15 @@ Difference:
 <dim>  }"
 `;
 
+exports[`.toEqual() {pass: false} expect(Set {}).not.toEqual(Set {}) 1`] = `
+"<dim>expect(<red>received</><dim>).not.toEqual(<green>expected</><dim>)
+
+Expected value to not equal:
+  <green>Set {}</>
+Received:
+  <red>Set {}</>"
+`;
+
 exports[`.toEqual() {pass: false} expect(Set {1, 2}).not.toEqual(Set {1, 2}) 1`] = `
 "<dim>expect(<red>received</><dim>).not.toEqual(<green>expected</><dim>)
 
diff --git a/packages/expect/src/__tests__/matchers.test.js b/packages/expect/src/__tests__/matchers.test.js
index 22ad6db509d0..260822431bc9 100644
--- a/packages/expect/src/__tests__/matchers.test.js
+++ b/packages/expect/src/__tests__/matchers.test.js
@@ -167,9 +167,14 @@ describe('.toEqual()', () => {
     [{a: 5}, {b: 6}],
     ['banana', 'apple'],
     [null, undefined],
+    [[1], [2]],
+    [[1, 2], [2, 1]],
+    [new Map(), new Set()],
     [new Set([1, 2]), new Set()],
     [new Set([1, 2]), new Set([1, 2, 3])],
     [new Map([[1, 'one'], [2, 'two']]), new Map([[1, 'one']])],
+    [new Map([['a', 0]]), new Map([['b', 0]])],
+    [new Map([['v', 1]]), new Map([['v', 2]])],
     [{a: 1, b: 2}, jestExpect.objectContaining({a: 2})],
     [false, jestExpect.objectContaining({a: 2})],
     [[1, 3], jestExpect.arrayContaining([1, 2])],
@@ -198,9 +203,14 @@ describe('.toEqual()', () => {
     [true, true],
     [1, 1],
     ['abc', 'abc'],
+    [[1], [1]],
+    [[1, 2], [1, 2]],
+    [{}, {}],
     [{a: 99}, {a: 99}],
+    [new Set(), new Set()],
     [new Set([1, 2]), new Set([1, 2])],
     [new Set([1, 2]), new Set([2, 1])],
+    [new Map(), new Map()],
     [new Map([[1, 'one'], [2, 'two']]), new Map([[1, 'one'], [2, 'two']])],
     [new Map([[1, 'one'], [2, 'two']]), new Map([[2, 'two'], [1, 'one']])],
     [{a: 1, b: 2}, jestExpect.objectContaining({a: 1})],
diff --git a/packages/expect/src/utils.js b/packages/expect/src/utils.js
index 750d26861cfc..e4067f83e918 100644
--- a/packages/expect/src/utils.js
+++ b/packages/expect/src/utils.js
@@ -8,7 +8,7 @@
  * @flow
  */
 
-import {equals} from './jasmine_utils';
+import {equals, isA} from './jasmine_utils';
 
 type GetPath = {
   hasEndProp?: boolean,
@@ -114,16 +114,29 @@ export const iterableEquality = (a: any, b: any) => {
   if (a.size !== undefined) {
     if (a.size !== b.size) {
       return false;
-    } else {
-      const args = [];
+    } else if (isA('Set', a)) {
+      let allFound = true;
       for (const aValue of a) {
-        args.push(aValue);
+        if (!b.has(aValue)) {
+          allFound = false;
+          break;
+        }
       }
-      for (const bValue of b) {
-        args.push(bValue);
+      if (allFound) {
+        return true;
+      }
+    } else if (isA('Map', a)) {
+      let allFound = true;
+      for (const aEntry of a) {
+        if (
+          !b.has(aEntry[0]) ||
+          !equals(aEntry[1], b.get(aEntry[0]), [iterableEquality])
+        ) {
+          allFound = false;
+          break;
+        }
       }
-      const merged = new a.constructor(args);
-      if (merged.size === a.size) {
+      if (allFound) {
         return true;
       }
     }