In myApi I used AbortController to ensure that any cancellable requests are aborted when a new cancellable request comes in:

let controller = new AbortController();

class client {
  axiosClient = axios.create({
    baseURL: example.com,
  });

  async post(url, data, config, stoppable) {
    let newConfig = {...config};

    // If this call can be cancelled, cancel any existing ones
    // and set up a new AbortController
    if (stoppable) {
      if (controller) {
        controller.abort();
      }
      // Add AbortSignal to the request config
      controller = new AbortController();
      newConfig = {...newConfig, signal: controller.signal};
    }
    return this.axiosClient.post(url, data, newConfig);
  }
}

export default new client();

Then in my component I pass in 'stoppable' as true; after the call I check whether the call was aborted or not. If not, I show the results; otherwise I ignore the response:

  useEffect(() => {
    const load = () => {

      const url = '/getDataForDate';

      const req = {
        selectedDate: moment(dateState.currentDate).format(
          'YYYY-MM-DD',
        ),
      };

      myApi
        .post(url, req, null, true)
        .then((res) => {
          if (!res.config.signal.aborted) {
            // Do something with the results
          }
        })
        .catch((err) => {
// Show an error if the request has failed entirely
        });
    };

    load();
  }, [dateState.currentDate]);

Axios does not support canceling requests at the moment. Please see this issue for details.

UPDATE: Cancellation support was added in axios v0.15.

EDIT: The axios cancel token API is based on the withdrawn cancelable promises proposal.

UPDATE 2022: Starting from v0.22.0 Axios supports AbortController to cancel requests in fetch API way:

Example:

const controller = new AbortController();

axios.get('/foo/bar', {
   signal: controller.signal
}).then(function(response) {
   //...
});
// cancel the request
controller.abort()

You can configure the timeout (default is about 5 seconds) and also can use this:

for adding a timeout:

const instance = axios.create({
  baseURL: 'https://some-domain.com/api/',
  timeout: 10000, // in miliseconds
  headers: {'X-Custom-Header': 'foobar'}
});

for axios v0.22.0:

const controller = new AbortController();
controller.abort()

for older versions:

CancelToken

Check this for more information