diff --git a/CHANGELOG.md b/CHANGELOG.md
index ec4926fe1557..d8a1714270f7 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,8 @@
 
 ### Features
 
+- `[expect]` Improve report when matcher fails, part 15 ([#8281](https://github.com/facebook/jest/pull/8281))
+
 ### Fixes
 
 - `[jest-snapshot]` Inline snapshots: do not indent empty lines ([#8277](https://github.com/facebook/jest/pull/8277))
diff --git a/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap b/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap
index b1234a0c609b..d565aa057f99 100644
--- a/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap
+++ b/packages/expect/src/__tests__/__snapshots__/matchers.test.js.snap
@@ -225,12 +225,7 @@ Received has value: <red>undefined</>"
 `;
 
 exports[`.toBe() does not crash on circular references 1`] = `
-"<dim>expect(</><red>received</><dim>).toBe(</><green>expected</><dim>) // Object.is equality</>
-
-Expected: <green>{}</>
-Received: <red>{\\"circular\\": [Circular]}</>
-
-Difference:
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
 <green>- Expected</>
 <red>+ Received</>
@@ -242,99 +237,137 @@ Difference:
 `;
 
 exports[`.toBe() fails for '"a"' with '.not' 1`] = `
-"<dim>expect(</><red>received</><dim>).</>not<dim>.toBe(</><green>expected</><dim>) // Object.is equality</>
+"<dim>expect(</><red>received</><dim>).</>not<dim>.</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
-Expected: <green>\\"a\\"</>
-Received: <red>\\"a\\"</>"
+Expected: not <green>\\"a\\"</>"
 `;
 
 exports[`.toBe() fails for '[]' with '.not' 1`] = `
-"<dim>expect(</><red>received</><dim>).</>not<dim>.toBe(</><green>expected</><dim>) // Object.is equality</>
+"<dim>expect(</><red>received</><dim>).</>not<dim>.</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
-Expected: <green>[]</>
-Received: <red>[]</>"
+Expected: not <green>[]</>"
 `;
 
 exports[`.toBe() fails for '{}' with '.not' 1`] = `
-"<dim>expect(</><red>received</><dim>).</>not<dim>.toBe(</><green>expected</><dim>) // Object.is equality</>
+"<dim>expect(</><red>received</><dim>).</>not<dim>.</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
-Expected: <green>{}</>
-Received: <red>{}</>"
+Expected: not <green>{}</>"
 `;
 
 exports[`.toBe() fails for '1' with '.not' 1`] = `
-"<dim>expect(</><red>received</><dim>).</>not<dim>.toBe(</><green>expected</><dim>) // Object.is equality</>
+"<dim>expect(</><red>received</><dim>).</>not<dim>.</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
-Expected: <green>1</>
-Received: <red>1</>"
+Expected: not <green>1</>"
 `;
 
 exports[`.toBe() fails for 'false' with '.not' 1`] = `
-"<dim>expect(</><red>received</><dim>).</>not<dim>.toBe(</><green>expected</><dim>) // Object.is equality</>
+"<dim>expect(</><red>received</><dim>).</>not<dim>.</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
-Expected: <green>false</>
-Received: <red>false</>"
+Expected: not <green>false</>"
 `;
 
 exports[`.toBe() fails for 'null' with '.not' 1`] = `
-"<dim>expect(</><red>received</><dim>).</>not<dim>.toBe(</><green>expected</><dim>) // Object.is equality</>
+"<dim>expect(</><red>received</><dim>).</>not<dim>.</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
-Expected: <green>null</>
-Received: <red>null</>"
+Expected: not <green>null</>"
 `;
 
 exports[`.toBe() fails for 'undefined' with '.not' 1`] = `
-"<dim>expect(</><red>received</><dim>).</>not<dim>.toBe(</><green>expected</><dim>) // Object.is equality</>
+"<dim>expect(</><red>received</><dim>).</>not<dim>.</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
-Expected: <green>undefined</>
-Received: <red>undefined</>"
+Expected: not <green>undefined</>"
 `;
 
 exports[`.toBe() fails for: "abc" and "cde" 1`] = `
-"<dim>expect(</><red>received</><dim>).toBe(</><green>expected</><dim>) // Object.is equality</>
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
 Expected: <green>\\"cde\\"</>
 Received: <red>\\"abc\\"</>"
 `;
 
+exports[`.toBe() fails for: "four
+4
+line
+string" and "3
+line
+string" 1`] = `
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
+
+<green>- Expected</>
+<red>+ Received</>
+
+<green>- 3</>
+<red>+ four</>
+<red>+ 4</>
+<dim>  line</>
+<dim>  string</>"
+`;
+
 exports[`.toBe() fails for: "with 
 trailing space" and "without trailing space" 1`] = `
-"<dim>expect(</><red>received</><dim>).toBe(</><green>expected</><dim>) // Object.is equality</>
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
 Expected: <green>\\"without trailing space\\"</>
 Received: <red>\\"with<inverse> </></>
 <red>trailing space\\"</>"
 `;
 
+exports[`.toBe() fails for: /received/ and /expected/ 1`] = `
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
+
+Expected: <green>/expected/</>
+Received: <red>/received/</>"
+`;
+
 exports[`.toBe() fails for: [] and [] 1`] = `
-"<dim>expect(</><red>received</><dim>).toBe(</><green>expected</><dim>) // Object.is equality</>
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
+
+<dim>If it should pass with deep equality, replace \\"toBe\\" with \\"toStrictEqual\\"</>
 
 Expected: <green>[]</>
-Received: <red>[]</>
+Received value has no visual difference"
+`;
 
-Difference:
+exports[`.toBe() fails for: [Error: received] and [Error: expected] 1`] = `
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
-<dim>Compared values have no visual difference.</> <dim>Note that you are testing for equality with the stricter \`toBe\` matcher using \`Object.is\`. For deep equality only, use \`toEqual\` instead.</>"
+Expected: <green>[Error: expected]</>
+Received: <red>[Error: received]</>"
 `;
 
-exports[`.toBe() fails for: {"a": 1} and {"a": 1} 1`] = `
-"<dim>expect(</><red>received</><dim>).toBe(</><green>expected</><dim>) // Object.is equality</>
+exports[`.toBe() fails for: [Function anonymous] and [Function anonymous] 1`] = `
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
-Expected: <green>{\\"a\\": 1}</>
-Received: <red>{\\"a\\": 1}</>
+Expected: <green>[Function anonymous]</>
+Received value has no visual difference"
+`;
 
-Difference:
+exports[`.toBe() fails for: {"a": [Function a], "b": 2} and {"a": Any<Function>, "b": 2} 1`] = `
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
+
+<dim>If it should pass with deep equality, replace \\"toBe\\" with \\"toStrictEqual\\"</>
 
-<dim>Compared values have no visual difference.</> <dim>Note that you are testing for equality with the stricter \`toBe\` matcher using \`Object.is\`. For deep equality only, use \`toEqual\` instead.</>"
+<green>- Expected</>
+<red>+ Received</>
+
+<dim>  Object {</>
+<green>-   \\"a\\": Any<Function>,</>
+<red>+   \\"a\\": [Function a],</>
+<dim>    \\"b\\": 2,</>
+<dim>  }</>"
 `;
 
-exports[`.toBe() fails for: {"a": 1} and {"a": 5} 1`] = `
-"<dim>expect(</><red>received</><dim>).toBe(</><green>expected</><dim>) // Object.is equality</>
+exports[`.toBe() fails for: {"a": 1} and {"a": 1} 1`] = `
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
-Expected: <green>{\\"a\\": 5}</>
-Received: <red>{\\"a\\": 1}</>
+<dim>If it should pass with deep equality, replace \\"toBe\\" with \\"toStrictEqual\\"</>
 
-Difference:
+Expected: <green>{\\"a\\": 1}</>
+Received value has no visual difference"
+`;
+
+exports[`.toBe() fails for: {"a": 1} and {"a": 5} 1`] = `
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
 <green>- Expected</>
 <red>+ Received</>
@@ -345,44 +378,75 @@ Difference:
 <dim>  }</>"
 `;
 
-exports[`.toBe() fails for: {} and {} 1`] = `
-"<dim>expect(</><red>received</><dim>).toBe(</><green>expected</><dim>) // Object.is equality</>
+exports[`.toBe() fails for: {"a": undefined, "b": 2} and {"b": 2} 1`] = `
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
-Expected: <green>{}</>
-Received: <red>{}</>
+<dim>If it should pass with deep equality, replace \\"toBe\\" with \\"toEqual\\"</>
 
-Difference:
+<green>- Expected</>
+<red>+ Received</>
+
+<dim>  Object {</>
+<red>+   \\"a\\": undefined,</>
+<dim>    \\"b\\": 2,</>
+<dim>  }</>"
+`;
 
-<dim>Compared values have no visual difference.</> <dim>Note that you are testing for equality with the stricter \`toBe\` matcher using \`Object.is\`. For deep equality only, use \`toEqual\` instead.</>"
+exports[`.toBe() fails for: {} and {} 1`] = `
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
+
+<dim>If it should pass with deep equality, replace \\"toBe\\" with \\"toStrictEqual\\"</>
+
+Expected: <green>{}</>
+Received value has no visual difference"
 `;
 
 exports[`.toBe() fails for: -0 and 0 1`] = `
-"<dim>expect(</><red>received</><dim>).toBe(</><green>expected</><dim>) // Object.is equality</>
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
 Expected: <green>0</>
 Received: <red>-0</>"
 `;
 
 exports[`.toBe() fails for: 1 and 2 1`] = `
-"<dim>expect(</><red>received</><dim>).toBe(</><green>expected</><dim>) // Object.is equality</>
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
 Expected: <green>2</>
 Received: <red>1</>"
 `;
 
-exports[`.toBe() fails for: null and undefined 1`] = `
-"<dim>expect(</><red>received</><dim>).toBe(</><green>expected</><dim>) // Object.is equality</>
+exports[`.toBe() fails for: 2020-02-20T00:00:00.000Z and 2020-02-20T00:00:00.000Z 1`] = `
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
-Expected: <green>undefined</>
-Received: <red>null</>
+<dim>If it should pass with deep equality, replace \\"toBe\\" with \\"toStrictEqual\\"</>
 
-Difference:
+Expected: <green>2020-02-20T00:00:00.000Z</>
+Received value has no visual difference"
+`;
+
+exports[`.toBe() fails for: 2020-02-21T00:00:00.000Z and 2020-02-20T00:00:00.000Z 1`] = `
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
-  Comparing two different types of values. Expected <green>undefined</> but received <red>null</>."
+Expected: <green>2020-02-20T00:00:00.000Z</>
+Received: <red>2020-02-21T00:00:00.000Z</>"
+`;
+
+exports[`.toBe() fails for: Symbol(received) and Symbol(expected) 1`] = `
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
+
+Expected: <green>Symbol(expected)</>
+Received: <red>Symbol(received)</>"
+`;
+
+exports[`.toBe() fails for: null and undefined 1`] = `
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
+
+Expected: <green>undefined</>
+Received: <red>null</>"
 `;
 
 exports[`.toBe() fails for: true and false 1`] = `
-"<dim>expect(</><red>received</><dim>).toBe(</><green>expected</><dim>) // Object.is equality</>
+"<dim>expect(</><red>received</><dim>).</>toBe<dim>(</><green>expected</><dim>) // Object.is equality</>
 
 Expected: <green>false</>
 Received: <red>true</>"
diff --git a/packages/expect/src/__tests__/matchers.test.js b/packages/expect/src/__tests__/matchers.test.js
index 953de2f2fcaf..9331fb30e6cb 100644
--- a/packages/expect/src/__tests__/matchers.test.js
+++ b/packages/expect/src/__tests__/matchers.test.js
@@ -203,11 +203,20 @@ describe('.toBe()', () => {
   [
     [1, 2],
     [true, false],
+    [() => {}, () => {}],
     [{}, {}],
     [{a: 1}, {a: 1}],
     [{a: 1}, {a: 5}],
+    [{a: () => {}, b: 2}, {a: expect.any(Function), b: 2}],
+    [{a: undefined, b: 2}, {b: 2}],
+    [new Date('2020-02-20'), new Date('2020-02-20')],
+    [new Date('2020-02-21'), new Date('2020-02-20')],
+    [/received/, /expected/],
+    [Symbol('received'), Symbol('expected')],
+    [new Error('received'), new Error('expected')],
     ['abc', 'cde'],
     ['with \ntrailing space', 'without trailing space'],
+    ['four\n4\nline\nstring', '3\nline\nstring'],
     [[], []],
     [null, undefined],
     [-0, +0],
diff --git a/packages/expect/src/matchers.ts b/packages/expect/src/matchers.ts
index 6b94eaf11d81..405b479330cc 100644
--- a/packages/expect/src/matchers.ts
+++ b/packages/expect/src/matchers.ts
@@ -8,9 +8,9 @@
 
 import getType, {isPrimitive} from 'jest-get-type';
 import {
+  DIM_COLOR,
   EXPECTED_COLOR,
   RECEIVED_COLOR,
-  SUGGEST_TO_EQUAL,
   SUGGEST_TO_CONTAIN_EQUAL,
   diff,
   ensureExpectedIsNonNegativeInteger,
@@ -22,6 +22,7 @@ import {
   printReceived,
   printExpected,
   printWithType,
+  stringify,
   MatcherHintOptions,
 } from 'jest-matcher-utils';
 import {MatchersObject, MatcherState} from './types';
@@ -41,6 +42,12 @@ import {
 } from './utils';
 import {equals} from './jasmineUtils';
 
+const toStrictEqualTesters = [
+  iterableEquality,
+  typeEquality,
+  sparseArrayEquality,
+];
+
 type ContainIterable =
   | Array<unknown>
   | Set<unknown>
@@ -50,10 +57,11 @@ type ContainIterable =
 
 const matchers: MatchersObject = {
   toBe(this: MatcherState, received: unknown, expected: unknown) {
-    const matcherName = '.toBe';
+    const matcherName = 'toBe';
     const options: MatcherHintOptions = {
       comment: 'Object.is equality',
       isNot: this.isNot,
+      promise: this.promise,
     };
 
     const pass = Object.is(received, expected);
@@ -62,32 +70,57 @@ const matchers: MatchersObject = {
       ? () =>
           matcherHint(matcherName, undefined, undefined, options) +
           '\n\n' +
-          `Expected: ${printExpected(expected)}\n` +
-          `Received: ${printReceived(received)}`
+          `Expected: not ${printExpected(expected)}`
       : () => {
           const receivedType = getType(received);
           const expectedType = getType(expected);
-          const suggestToEqual =
-            receivedType === expectedType &&
-            (receivedType === 'object' || expectedType === 'array') &&
-            equals(received, expected, [iterableEquality]);
-          const oneline = isOneline(expected, received);
-          const diffString = diff(expected, received, {expand: this.expand});
+
+          let deepEqualityName = null;
+          if (expectedType !== 'map' && expectedType !== 'set') {
+            // If deep equality passes when referential identity fails,
+            // but exclude map and set until review of their equality logic.
+            if (equals(received, expected, toStrictEqualTesters, true)) {
+              deepEqualityName = 'toStrictEqual';
+            } else if (equals(received, expected, [iterableEquality])) {
+              deepEqualityName = 'toEqual';
+            }
+          }
+
+          const hasConciseReport =
+            receivedType !== expectedType ||
+            (isPrimitive(expected) &&
+              (expectedType !== 'string' || isOneline(expected, received))) ||
+            expectedType === 'date' ||
+            expectedType === 'function' ||
+            expectedType === 'regexp' ||
+            (received instanceof Error && expected instanceof Error);
+          const hasDifference = stringify(expected) !== stringify(received);
+          const difference =
+            !hasConciseReport && hasDifference
+              ? diff(expected, received, {expand: this.expand}) // string | null
+              : null;
 
           return (
             matcherHint(matcherName, undefined, undefined, options) +
             '\n\n' +
-            `Expected: ${printExpected(expected)}\n` +
-            `Received: ${printReceived(received)}` +
-            (diffString && !oneline ? `\n\nDifference:\n\n${diffString}` : '') +
-            (suggestToEqual ? ` ${SUGGEST_TO_EQUAL}` : '')
+            (deepEqualityName !== null
+              ? DIM_COLOR(
+                  `If it should pass with deep equality, replace "${matcherName}" with "${deepEqualityName}"`,
+                ) + '\n\n'
+              : '') +
+            (difference !== null
+              ? difference
+              : `Expected: ${printExpected(expected)}\n` +
+                (hasDifference
+                  ? `Received: ${printReceived(received)}`
+                  : 'Received value has no visual difference'))
           );
         };
 
     // Passing the actual and expected objects so that a custom reporter
     // could access them, for example in order to display a custom visual diff,
     // or create a different error message
-    return {actual: received, expected, message, name: 'toBe', pass};
+    return {actual: received, expected, message, name: matcherName, pass};
   },
 
   toBeCloseTo(
@@ -856,12 +889,7 @@ const matchers: MatchersObject = {
       isNot: this.isNot,
     };
 
-    const pass = equals(
-      received,
-      expected,
-      [iterableEquality, typeEquality, sparseArrayEquality],
-      true,
-    );
+    const pass = equals(received, expected, toStrictEqualTesters, true);
 
     const message = pass
       ? () =>
diff --git a/packages/jest-matcher-utils/src/index.ts b/packages/jest-matcher-utils/src/index.ts
index 89fd60568e6b..9f9de13390ce 100644
--- a/packages/jest-matcher-utils/src/index.ts
+++ b/packages/jest-matcher-utils/src/index.ts
@@ -41,7 +41,7 @@ export const EXPECTED_COLOR = chalk.green;
 export const RECEIVED_COLOR = chalk.red;
 export const INVERTED_COLOR = chalk.inverse;
 export const BOLD_WEIGHT = chalk.bold;
-const DIM_COLOR = chalk.dim;
+export const DIM_COLOR = chalk.dim;
 
 const NUMBERS = [
   'zero',
@@ -60,10 +60,6 @@ const NUMBERS = [
   'thirteen',
 ];
 
-export const SUGGEST_TO_EQUAL = chalk.dim(
-  'Note that you are testing for equality with the stricter `toBe` matcher using `Object.is`. For deep equality only, use `toEqual` instead.',
-);
-
 export const SUGGEST_TO_CONTAIN_EQUAL = chalk.dim(
   'Looks like you wanted to test for object/array equality with the stricter `toContain` matcher. You probably need to use `toContainEqual` instead.',
 );