How to work with ajax events?

How to work with ajax events?

Here's the reference documentation that I've been following:  http://api.jquery.com/Ajax_Events/ and  http://api.jquery.com/ajaxSuccess/

The first link indicates that I can bind through "jQuery.on()" any DOM element to handle an ajax event. The second link indicates that this is invalid since 1.8.

As a newbie to jQuery... how do I handle an ajax event other than just binding to jQuery(document)?