EventSource. From there you can add an event listener for new messages. Here’s an example that uses jQuery to append an item to a list.
var source = new EventSource(
$('#events-list').append('<li>' + e + </li>');
For back-end services, an SSE stream is just a normal HTTP request that stays open, so whatever library you are currently using for making the other API requests should work fine. You will just have to handle the data differently since the connection does not close.