diff --git a/CHANGELOG.md b/CHANGELOG.md
index 9c7acc04eb1e..2f88fddfdada 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -150,6 +150,8 @@
   configuration ([#5976](https://github.com/facebook/jest/pull/5976))
 * `[website]` Fix website docs
   ([#5853](https://github.com/facebook/jest/pull/5853))
+* `[expect]` Fix isEqual Set and Map to compare object values and keys
+  regardless of order ([#6150](https://github.com/facebook/jest/pull/6150))
 
 ### Chore & Maintenance
 
diff --git a/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap b/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap
index 711f01c60f77..5dd69d14b74e 100644
--- a/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap
+++ b/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap
@@ -2295,6 +2295,88 @@ Difference:
 <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 {</>
+<dim>    Array [</>
+<dim>      \\"v\\",</>
+<green>-   ] => 2,</>
+<red>+   ] => 1,</>
+<dim>  }</>"
+`;
+
+exports[`.toEqual() {pass: false} expect(Map {[1] => "one", [2] => "two", [3] => "three", [3] => "four"}).not.toEqual(Map {[3] => "three", [3] => "four", [2] => "two", [1] => "one"}) 1`] = `
+"<dim>expect(</><red>received</><dim>).not.toEqual(</><green>expected</><dim>)</>
+
+Expected value to not equal:
+  <green>Map {[3] => \\"three\\", [3] => \\"four\\", [2] => \\"two\\", [1] => \\"one\\"}</>
+Received:
+  <red>Map {[1] => \\"one\\", [2] => \\"two\\", [3] => \\"three\\", [3] => \\"four\\"}</>"
+`;
+
+exports[`.toEqual() {pass: false} expect(Map {[1] => "one", [2] => "two"}).not.toEqual(Map {[2] => "two", [1] => "one"}) 1`] = `
+"<dim>expect(</><red>received</><dim>).not.toEqual(</><green>expected</><dim>)</>
+
+Expected value to not equal:
+  <green>Map {[2] => \\"two\\", [1] => \\"one\\"}</>
+Received:
+  <red>Map {[1] => \\"one\\", [2] => \\"two\\"}</>"
+`;
+
+exports[`.toEqual() {pass: false} expect(Map {[1] => Map {[1] => "one"}, [2] => Map {[2] => "two"}}).not.toEqual(Map {[2] => Map {[2] => "two"}, [1] => Map {[1] => "one"}}) 1`] = `
+"<dim>expect(</><red>received</><dim>).not.toEqual(</><green>expected</><dim>)</>
+
+Expected value to not equal:
+  <green>Map {[2] => Map {[2] => \\"two\\"}, [1] => Map {[1] => \\"one\\"}}</>
+Received:
+  <red>Map {[1] => Map {[1] => \\"one\\"}, [2] => Map {[2] => \\"two\\"}}</>"
+`;
+
+exports[`.toEqual() {pass: false} expect(Map {[1] => Map {[1] => "one"}}).toEqual(Map {[1] => Map {[1] => "two"}}) 1`] = `
+"<dim>expect(</><red>received</><dim>).toEqual(</><green>expected</><dim>)</>
+
+Expected value to equal:
+  <green>Map {[1] => Map {[1] => \\"two\\"}}</>
+Received:
+  <red>Map {[1] => Map {[1] => \\"one\\"}}</>
+
+Difference:
+
+<green>- Expected</>
+<red>+ Received</>
+
+<yellow>@@ -2,8 +2,8 @@</>
+<dim>    Array [</>
+<dim>      1,</>
+<dim>    ] => Map {</>
+<dim>      Array [</>
+<dim>        1,</>
+<green>-     ] => \\"two\\",</>
+<red>+     ] => \\"one\\",</>
+<dim>    },</>
+<dim>  }</>"
+`;
+
+exports[`.toEqual() {pass: false} expect(Map {{"a": 1} => "one", {"b": 2} => "two"}).not.toEqual(Map {{"b": 2} => "two", {"a": 1} => "one"}) 1`] = `
+"<dim>expect(</><red>received</><dim>).not.toEqual(</><green>expected</><dim>)</>
+
+Expected value to not equal:
+  <green>Map {{\\"b\\": 2} => \\"two\\", {\\"a\\": 1} => \\"one\\"}</>
+Received:
+  <red>Map {{\\"a\\": 1} => \\"one\\", {\\"b\\": 2} => \\"two\\"}</>"
+`;
+
 exports[`.toEqual() {pass: false} expect(Map {}).not.toEqual(Map {}) 1`] = `
 "<dim>expect(</><red>received</><dim>).not.toEqual(</><green>expected</><dim>)</>
 
@@ -2354,6 +2436,92 @@ Difference:
 <dim>  }</>"
 `;
 
+exports[`.toEqual() {pass: false} expect(Map {1 => ["one"], 2 => ["two"]}).not.toEqual(Map {2 => ["two"], 1 => ["one"]}) 1`] = `
+"<dim>expect(</><red>received</><dim>).not.toEqual(</><green>expected</><dim>)</>
+
+Expected value to not equal:
+  <green>Map {2 => [\\"two\\"], 1 => [\\"one\\"]}</>
+Received:
+  <red>Map {1 => [\\"one\\"], 2 => [\\"two\\"]}</>"
+`;
+
+exports[`.toEqual() {pass: false} expect(Set {[1], [2], [3], [3]}).not.toEqual(Set {[3], [3], [2], [1]}) 1`] = `
+"<dim>expect(</><red>received</><dim>).not.toEqual(</><green>expected</><dim>)</>
+
+Expected value to not equal:
+  <green>Set {[3], [3], [2], [1]}</>
+Received:
+  <red>Set {[1], [2], [3], [3]}</>"
+`;
+
+exports[`.toEqual() {pass: false} expect(Set {[1], [2]}).not.toEqual(Set {[2], [1]}) 1`] = `
+"<dim>expect(</><red>received</><dim>).not.toEqual(</><green>expected</><dim>)</>
+
+Expected value to not equal:
+  <green>Set {[2], [1]}</>
+Received:
+  <red>Set {[1], [2]}</>"
+`;
+
+exports[`.toEqual() {pass: false} expect(Set {[1], [2]}).toEqual(Set {[1], [2], [2]}) 1`] = `
+"<dim>expect(</><red>received</><dim>).toEqual(</><green>expected</><dim>)</>
+
+Expected value to equal:
+  <green>Set {[1], [2], [2]}</>
+Received:
+  <red>Set {[1], [2]}</>
+
+Difference:
+
+<green>- Expected</>
+<red>+ Received</>
+
+<yellow>@@ -3,9 +3,6 @@</>
+<dim>      1,</>
+<dim>    ],</>
+<dim>    Array [</>
+<dim>      2,</>
+<dim>    ],</>
+<green>-   Array [</>
+<green>-     2,</>
+<green>-   ],</>
+<dim>  }</>"
+`;
+
+exports[`.toEqual() {pass: false} expect(Set {[1], [2]}).toEqual(Set {[1], [2], [3]}) 1`] = `
+"<dim>expect(</><red>received</><dim>).toEqual(</><green>expected</><dim>)</>
+
+Expected value to equal:
+  <green>Set {[1], [2], [3]}</>
+Received:
+  <red>Set {[1], [2]}</>
+
+Difference:
+
+<green>- Expected</>
+<red>+ Received</>
+
+<yellow>@@ -3,9 +3,6 @@</>
+<dim>      1,</>
+<dim>    ],</>
+<dim>    Array [</>
+<dim>      2,</>
+<dim>    ],</>
+<green>-   Array [</>
+<green>-     3,</>
+<green>-   ],</>
+<dim>  }</>"
+`;
+
+exports[`.toEqual() {pass: false} expect(Set {{"a": 1}, {"b": 2}}).not.toEqual(Set {{"b": 2}, {"a": 1}}) 1`] = `
+"<dim>expect(</><red>received</><dim>).not.toEqual(</><green>expected</><dim>)</>
+
+Expected value to not equal:
+  <green>Set {{\\"b\\": 2}, {\\"a\\": 1}}</>
+Received:
+  <red>Set {{\\"a\\": 1}, {\\"b\\": 2}}</>"
+`;
+
 exports[`.toEqual() {pass: false} expect(Set {}).not.toEqual(Set {}) 1`] = `
 "<dim>expect(</><red>received</><dim>).not.toEqual(</><green>expected</><dim>)</>
 
@@ -2421,6 +2589,39 @@ Difference:
 <dim>  }</>"
 `;
 
+exports[`.toEqual() {pass: false} expect(Set {Set {[1]}, Set {[2]}}).not.toEqual(Set {Set {[2]}, Set {[1]}}) 1`] = `
+"<dim>expect(</><red>received</><dim>).not.toEqual(</><green>expected</><dim>)</>
+
+Expected value to not equal:
+  <green>Set {Set {[2]}, Set {[1]}}</>
+Received:
+  <red>Set {Set {[1]}, Set {[2]}}</>"
+`;
+
+exports[`.toEqual() {pass: false} expect(Set {Set {1}, Set {2}}).toEqual(Set {Set {1}, Set {3}}) 1`] = `
+"<dim>expect(</><red>received</><dim>).toEqual(</><green>expected</><dim>)</>
+
+Expected value to equal:
+  <green>Set {Set {1}, Set {3}}</>
+Received:
+  <red>Set {Set {1}, Set {2}}</>
+
+Difference:
+
+<green>- Expected</>
+<red>+ Received</>
+
+<dim>  Set {</>
+<dim>    Set {</>
+<dim>      1,</>
+<dim>    },</>
+<dim>    Set {</>
+<green>-     3,</>
+<red>+     2,</>
+<dim>    },</>
+<dim>  }</>"
+`;
+
 exports[`.toEqual() {pass: false} expect(false).toEqual(ObjectContaining {"a": 2}) 1`] = `
 "<dim>expect(</><red>received</><dim>).toEqual(</><green>expected</><dim>)</>
 
diff --git a/packages/expect/src/__tests__/matchers.test.js b/packages/expect/src/__tests__/matchers.test.js
index 2e9c8a300e2b..2b2d142f85f5 100644
--- a/packages/expect/src/__tests__/matchers.test.js
+++ b/packages/expect/src/__tests__/matchers.test.js
@@ -247,12 +247,23 @@ describe('.toEqual()', () => {
     [new Map(), new Set()],
     [new Set([1, 2]), new Set()],
     [new Set([1, 2]), new Set([1, 2, 3])],
+    [new Set([[1], [2]]), new Set([[1], [2], [3]])],
+    [new Set([[1], [2]]), new Set([[1], [2], [2]])],
+    [
+      new Set([new Set([1]), new Set([2])]),
+      new Set([new Set([1]), new Set([3])]),
+    ],
     [Immutable.Set([1, 2]), Immutable.Set()],
     [Immutable.Set([1, 2]), Immutable.Set([1, 2, 3])],
     [Immutable.OrderedSet([1, 2]), Immutable.OrderedSet([2, 1])],
     [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]])],
+    [new Map([[['v'], 1]]), new Map([[['v'], 2]])],
+    [
+      new Map([[[1], new Map([[[1], 'one']])]]),
+      new Map([[[1], new Map([[[1], 'two']])]]),
+    ],
     [Immutable.Map({a: 0}), Immutable.Map({b: 0})],
     [Immutable.Map({v: 1}), Immutable.Map({v: 2})],
     [
@@ -304,6 +315,13 @@ describe('.toEqual()', () => {
     [new Set(), new Set()],
     [new Set([1, 2]), new Set([1, 2])],
     [new Set([1, 2]), new Set([2, 1])],
+    [new Set([[1], [2]]), new Set([[2], [1]])],
+    [
+      new Set([new Set([[1]]), new Set([[2]])]),
+      new Set([new Set([[2]]), new Set([[1]])]),
+    ],
+    [new Set([[1], [2], [3], [3]]), new Set([[3], [3], [2], [1]])],
+    [new Set([{a: 1}, {b: 2}]), new Set([{b: 2}, {a: 1}])],
     [Immutable.Set(), Immutable.Set()],
     [Immutable.Set([1, 2]), Immutable.Set([1, 2])],
     [Immutable.Set([1, 2]), Immutable.Set([2, 1])],
@@ -312,6 +330,26 @@ describe('.toEqual()', () => {
     [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']])],
+    [
+      new Map([[[1], 'one'], [[2], 'two'], [[3], 'three'], [[3], 'four']]),
+      new Map([[[3], 'three'], [[3], 'four'], [[2], 'two'], [[1], 'one']]),
+    ],
+    [
+      new Map([[[1], new Map([[[1], 'one']])], [[2], new Map([[[2], 'two']])]]),
+      new Map([[[2], new Map([[[2], 'two']])], [[1], new Map([[[1], 'one']])]]),
+    ],
+    [
+      new Map([[[1], 'one'], [[2], 'two']]),
+      new Map([[[2], 'two'], [[1], 'one']]),
+    ],
+    [
+      new Map([[{a: 1}, 'one'], [{b: 2}, 'two']]),
+      new Map([[{b: 2}, 'two'], [{a: 1}, 'one']]),
+    ],
+    [
+      new Map([[1, ['one']], [2, ['two']]]),
+      new Map([[2, ['two']], [1, ['one']]]),
+    ],
     [Immutable.Map(), Immutable.Map()],
     [
       Immutable.Map()
diff --git a/packages/expect/src/utils.js b/packages/expect/src/utils.js
index a6cc277952e6..0d8c38cfa787 100644
--- a/packages/expect/src/utils.js
+++ b/packages/expect/src/utils.js
@@ -128,8 +128,18 @@ export const iterableEquality = (a: any, b: any) => {
       let allFound = true;
       for (const aValue of a) {
         if (!b.has(aValue)) {
-          allFound = false;
-          break;
+          let has = false;
+          for (const bValue of b) {
+            const isEqual = equals(aValue, bValue, [iterableEquality]);
+            if (isEqual === true) {
+              has = true;
+            }
+          }
+
+          if (has === false) {
+            allFound = false;
+            break;
+          }
         }
       }
       if (allFound) {
@@ -142,8 +152,24 @@ export const iterableEquality = (a: any, b: any) => {
           !b.has(aEntry[0]) ||
           !equals(aEntry[1], b.get(aEntry[0]), [iterableEquality])
         ) {
-          allFound = false;
-          break;
+          let has = false;
+          for (const bEntry of b) {
+            const matchedKey = equals(aEntry[0], bEntry[0], [iterableEquality]);
+
+            let matchedValue = false;
+            if (matchedKey === true) {
+              matchedValue = equals(aEntry[1], bEntry[1], [iterableEquality]);
+            }
+
+            if (matchedValue === true) {
+              has = true;
+            }
+          }
+
+          if (has === false) {
+            allFound = false;
+            break;
+          }
         }
       }
       if (allFound) {