XMLHttpRequest (AJAX) is introduced for historical purposes, and as a way to illustrate the need for Promises.

To perform REST accesses in a browser (and any other HTTP accesses, and accesses with other protocols), the basic class used is XMLHttpRequest.

XMLHttpRequest (XHR) implements what is known as AJAX (Asynchronous Javascript and XML)

For example, the code below reads the details of an imgur album. The colors/underlining indicate the HTTP method, path, headers, request data (null = nothing in this case), response code, and response data.

var http=new XMLHttpRequest();
http.open("GET", "https://api.imgur.com/3/album/xQY8w", true);
http.setRequestHeader("authorization", "Client-ID SECRET");
http.onreadystatechange = function() {
    if(http.readyState === 4) 
      if(http.status === 200){
         // here the API call result is known
         console.log(http.responseText);
      }else{
         console.error(http.statusText);
      }
}
http.send(null);
// here the API call result is unknown

As you can see, to avoid our code from blocking, we have to assign a callback to the http request. This callback will be called every time the readyState of the http request changes. The readyState indicates:

request was open
request was sent and the response headers arrived (remember the empty line after the headers in the HTTP protocol?),
waiting for the response data transfer to complete
response is complete (all response data was received)

Everything that you want to do after the response has arrived must be in this callback. http.send() returns immediately, i.e. before the API call result is known!

HTTP POST via XMLHttpRequest

A POST (or PUT) call will pass some data to the server as the send() parameter. In order for the data that is sent to the server to be encoded like the data in a HTML <form> we can use the FormData class (note: other APIs may require to send the data in JSON! Check your API documentation!). Here is how we can upload an imgur image.

var fd = new FormData();
fd.append("image", IMAGE_BYTES);
fd.append("album", ALBUM_DELETE_HASH);

var http=new XMLHttpRequest();
http.open("POST", "https://api.imgur.com/3/image", true);
http.setRequestHeader("authorization", "Client-ID SECRET");
http.onreadystatechange = function() {
    if(http.readyState === 4) 
      if(http.status === 200){
         // here the API call result is known
         console.log(http.responseText);
      }else{
        console.error(http.statusText);
      }
}
http.send(fd);
// here the API call result is unknown