diff --git a/README.md b/README.md
index 4e2361ee..7cd44fca 100644
--- a/README.md
+++ b/README.md
@@ -68,6 +68,7 @@ clear to read and to maintain.
   - [`toHaveValue`](#tohavevalue)
   - [`toHaveDisplayValue`](#tohavedisplayvalue)
   - [`toBeChecked`](#tobechecked)
+  - [`toHaveDescription`](#tohavedescription)
 - [Deprecated matchers](#deprecated-matchers)
   - [`toBeInTheDOM`](#tobeinthedom)
 - [Inspiration](#inspiration)
@@ -86,9 +87,11 @@ should be installed as one of your project's `devDependencies`:
 ```
 npm install --save-dev @testing-library/jest-dom
 ```
-or 
+
+or
 
 for installation with [yarn](https://yarnpkg.com/) package manager.
+
 ```
 yarn add --dev @testing-library/jest-dom
 ```
@@ -725,7 +728,7 @@ const element = getByTestId('text-content')
 
 expect(element).toHaveTextContent('Content')
 expect(element).toHaveTextContent(/^Text Content$/) // to match the whole content
-expect(element).toHaveTextContent(/content$/i) // to use case-insentive match
+expect(element).toHaveTextContent(/content$/i) // to use case-insensitive match
 expect(element).not.toHaveTextContent('content')
 ```
 
@@ -886,6 +889,60 @@ expect(ariaSwitchChecked).toBeChecked()
 expect(ariaSwitchUnchecked).not.toBeChecked()
 ```
 
+<hr />
+
+### `toHaveDescription`
+
+```typescript
+toHaveDescription(text: string | RegExp)
+```
+
+This allows you to check whether the given element has a description or not.
+
+An element gets its description via the
+[`aria-describedby` attribute](https://developer.mozilla.org/en-US/docs/Web/Accessibility/ARIA/ARIA_Techniques/Using_the_aria-describedby_attribute).
+Set this to the `id` of one or more other elements. These elements may be nested
+inside, be outside, or a sibling of the passed in element.
+
+Whitespace is normalized. Using multiple ids will
+[join the referenced elements’ text content separated by a space](https://www.w3.org/TR/accname-1.1/#mapping_additional_nd_description).
+
+When a `string` argument is passed through, it will perform a whole
+case-sensitive match to the description text.
+
+To perform a case-insensitive match, you can use a `RegExp` with the `/i`
+modifier.
+
+To perform a partial match, you can pass a `RegExp` or use
+`expect.stringContaining("partial string")`.
+
+#### Examples
+
+```html
+<button aria-label="Close" aria-describedby="description-close">
+  X
+</button>
+<div id="description-close">
+  Closing will discard any changes
+</div>
+
+<button>Delete</button>
+```
+
+```javascript
+const closeButton = getByRole('button', {name: 'Close'})
+
+expect(closeButton).toHaveDescription('Closing will discard any changes')
+expect(closeButton).toHaveDescription(/will discard/) // to partially match
+expect(closeButton).toHaveDescription(expect.stringContaining('will discard')) // to partially match
+expect(closeButton).toHaveDescription(/^closing/i) // to use case-insensitive match
+expect(closeButton).not.toHaveDescription('Other description')
+
+const deleteButton = getByRole('button', {name: 'Delete'})
+expect(deleteButton).not.toHaveDescription()
+expect(deleteButton).toHaveDescription('') // Missing or empty description always becomes a blank string
+```
+
 ## Deprecated matchers
 
 ### `toBeInTheDOM`
@@ -1026,6 +1083,7 @@ Thanks goes to these people ([emoji key][emojis]):
 
 <!-- markdownlint-enable -->
 <!-- prettier-ignore-end -->
+
 <!-- ALL-CONTRIBUTORS-LIST:END -->
 
 This project follows the [all-contributors][all-contributors] specification.
diff --git a/src/__tests__/helpers/test-utils.js b/src/__tests__/helpers/test-utils.js
index 3efabeac..2133b163 100644
--- a/src/__tests__/helpers/test-utils.js
+++ b/src/__tests__/helpers/test-utils.js
@@ -5,6 +5,12 @@ function render(html) {
   container.innerHTML = html
   const queryByTestId = testId =>
     container.querySelector(`[data-testid="${testId}"]`)
+
+  // Some tests need to look up global ids with document.getElementById()
+  // so we need to be inside an actual document.
+  document.body.innerHTML = ''
+  document.body.appendChild(container)
+
   return {container, queryByTestId}
 }
 
diff --git a/src/__tests__/to-have-description.js b/src/__tests__/to-have-description.js
new file mode 100644
index 00000000..ffb10032
--- /dev/null
+++ b/src/__tests__/to-have-description.js
@@ -0,0 +1,138 @@
+import {render} from './helpers/test-utils'
+
+describe('.toHaveDescription', () => {
+  test('handles positive test cases', () => {
+    const {queryByTestId} = render(`
+    <div id="description">The description</div>
+
+    <div data-testid="single" aria-describedby="description"></div>
+    <div data-testid="invalid_id" aria-describedby="invalid"></div>
+    <div data-testid="without"></div>
+    `)
+
+    expect(queryByTestId('single')).toHaveDescription('The description')
+    expect(queryByTestId('single')).toHaveDescription(
+      expect.stringContaining('The'),
+    )
+    expect(queryByTestId('single')).toHaveDescription(/The/)
+    expect(queryByTestId('single')).toHaveDescription(
+      expect.stringMatching(/The/),
+    )
+    expect(queryByTestId('single')).toHaveDescription(/description/)
+    expect(queryByTestId('single')).not.toHaveDescription('Something else')
+    expect(queryByTestId('single')).not.toHaveDescription('The')
+
+    expect(queryByTestId('invalid_id')).not.toHaveDescription()
+    expect(queryByTestId('invalid_id')).toHaveDescription('')
+
+    expect(queryByTestId('without')).not.toHaveDescription()
+    expect(queryByTestId('without')).toHaveDescription('')
+  })
+
+  test('handles multiple ids', () => {
+    const {queryByTestId} = render(`
+    <div id="first">First description</div>
+    <div id="second">Second description</div>
+    <div id="third">Third description</div>
+
+    <div data-testid="multiple" aria-describedby="first second third"></div>
+    `)
+
+    expect(queryByTestId('multiple')).toHaveDescription(
+      'First description Second description Third description',
+    )
+    expect(queryByTestId('multiple')).toHaveDescription(
+      /Second description Third/,
+    )
+    expect(queryByTestId('multiple')).toHaveDescription(
+      expect.stringContaining('Second description Third'),
+    )
+    expect(queryByTestId('multiple')).toHaveDescription(
+      expect.stringMatching(/Second description Third/),
+    )
+    expect(queryByTestId('multiple')).not.toHaveDescription('Something else')
+    expect(queryByTestId('multiple')).not.toHaveDescription('First')
+  })
+
+  test('handles negative test cases', () => {
+    const {queryByTestId} = render(`
+    <div id="description">The description</div>
+    <div data-testid="target" aria-describedby="description"></div>
+    `)
+
+    expect(() =>
+      expect(queryByTestId('other')).toHaveDescription('The description'),
+    ).toThrowError()
+
+    expect(() =>
+      expect(queryByTestId('target')).toHaveDescription('Something else'),
+    ).toThrowError()
+
+    expect(() =>
+      expect(queryByTestId('target')).not.toHaveDescription('The description'),
+    ).toThrowError()
+  })
+
+  test('normalizes whitespace', () => {
+    const {queryByTestId} = render(`
+      <div id="first">
+        Step
+          1
+            of
+              4
+      </div>
+      <div id="second">
+        And
+          extra
+            description
+      </div>
+      <div data-testid="target" aria-describedby="first second"></div>
+    `)
+
+    expect(queryByTestId('target')).toHaveDescription(
+      'Step 1 of 4 And extra description',
+    )
+  })
+
+  test('can handle multiple levels with content spread across decendants', () => {
+    const {queryByTestId} = render(`
+        <span id="description">
+            <span>Step</span>
+            <span>      1</span>
+            <span><span>of</span></span>
+
+
+            4</span>
+        </span>
+        <div data-testid="target" aria-describedby="description"></div>
+    `)
+
+    expect(queryByTestId('target')).toHaveDescription('Step 1 of 4')
+  })
+
+  test('handles extra whitespace with multiple ids', () => {
+    const {queryByTestId} = render(`
+    <div id="first">First description</div>
+    <div id="second">Second description</div>
+    <div id="third">Third description</div>
+
+    <div data-testid="multiple" aria-describedby="  first
+    second    third
+    "></div>
+    `)
+
+    expect(queryByTestId('multiple')).toHaveDescription(
+      'First description Second description Third description',
+    )
+  })
+
+  test('is case-sensitive', () => {
+    const {queryByTestId} = render(`
+      <span id="description">Sensitive text</span>
+      <div data-testid="target" aria-describedby="description"></div>
+    `)
+
+    expect(queryByTestId('target')).toHaveDescription('Sensitive text')
+    expect(queryByTestId('target')).not.toHaveDescription('sensitive text')
+  })
+})
diff --git a/src/matchers.js b/src/matchers.js
index 552f1300..703dd18c 100644
--- a/src/matchers.js
+++ b/src/matchers.js
@@ -16,6 +16,7 @@ import {toBeInvalid, toBeValid} from './to-be-invalid'
 import {toHaveValue} from './to-have-value'
 import {toHaveDisplayValue} from './to-have-display-value'
 import {toBeChecked} from './to-be-checked'
+import {toHaveDescription} from './to-have-description'
 
 export {
   toBeInTheDOM,
@@ -38,4 +39,5 @@ export {
   toHaveValue,
   toHaveDisplayValue,
   toBeChecked,
+  toHaveDescription,
 }
diff --git a/src/to-have-description.js b/src/to-have-description.js
new file mode 100644
index 00000000..1f1f769b
--- /dev/null
+++ b/src/to-have-description.js
@@ -0,0 +1,42 @@
+import {matcherHint, printExpected, printReceived} from 'jest-matcher-utils'
+import {checkHtmlElement, getMessage, normalize} from './utils'
+
+// See algoritm: https://www.w3.org/TR/accname-1.1/#mapping_additional_nd_description
+export function toHaveDescription(htmlElement, checkWith) {
+  checkHtmlElement(htmlElement, toHaveDescription, this)
+
+  const expectsDescription = checkWith !== undefined
+
+  const descriptionIDRaw = htmlElement.getAttribute('aria-describedby') || ''
+  const descriptionIDs = descriptionIDRaw.split(/\s+/).filter(Boolean)
+  let description = ''
+  if (descriptionIDs.length > 0) {
+    const document = htmlElement.ownerDocument
+    const descriptionEls = descriptionIDs
+      .map(descriptionID => document.getElementById(descriptionID))
+      .filter(Boolean)
+    description = normalize(descriptionEls.map(el => el.textContent).join(' '))
+  }
+
+  return {
+    pass: expectsDescription
+      ? checkWith instanceof RegExp
+        ? checkWith.test(description)
+        : this.equals(description, checkWith)
+      : Boolean(description),
+    message: () => {
+      const to = this.isNot ? 'not to' : 'to'
+      return getMessage(
+        matcherHint(
+          `${this.isNot ? '.not' : ''}.toHaveDescription`,
+          'element',
+          '',
+        ),
+        `Expected the element ${to} have description`,
+        printExpected(checkWith),
+        'Received',
+        printReceived(description),
+      )
+    },
+  }
+}