Question: How do I check if a component is not present, i.e. that a specific component has not been rendered?

Answer: 
If you're using [react-testing-library](https://testing-library.com/docs/dom-testing-library/api-queries#queryby) (I know the OP wasn't but I found this question via web search) then this will work:

```
expect(component.queryByText("Text I care about")).not.toBeInTheDocument();

```

You can query by `Text`, `Role`, and several others. See [docs](https://testing-library.com/docs/dom-testing-library/api-queries#queryby) for more info.

**Note:** `queryBy*` will return `null` if it is not found. If you use `getBy*` then it will error out for elements not found.
Providing a slightly updated answer based on [the documentation for enzyme-matchers's `toExist`](https://github.com/FormidableLabs/enzyme-matchers/blob/master/packages/jest-enzyme/README.md#toexist). This will require you to install the `enzyme-matchers` package.

```
function Fixture() {
  return (
    <div>
      <span className="foo" />
      <span className="bar baz" />
    </div>
  );
}

const wrapper = mount(<Fixture />); // mount/render/shallow when applicable

expect(wrapper.find('span')).toExist();
expect(wrapper.find('ul')).not.toExist();

```