Shedding some light on Ajax (Asynchronous JavaScript and XML)
Not only is Ajax a dominant Dutch football club that's won the Champions League 4 times and a household cleaner, it's also a web technology. Actually, it's a collection, or suite, of web technologies (you might have noticed that JavaScript and XML are both in the title). As such, the pieces of the puzzle were already in place before Jesse James Garrett pulled them together in 2005 and there's some overlap here between the JavaScript and XML pages I've put together. I have tried on this page to be specific to Ajax and not it's components. What's significant about Ajax is the "paradigm shift" that it represents (Matlis).
The bottom line on usability:
Because Ajax is designed with W3C recommendations in mind it works well accross browsers. However, since Ajax is really a suite and not just one tool, expect to spend a lot of time learning if you don't already know JavaScript and XML.
More on Usability:
Since Ajax is so complicated, whether an example will work on a browser is more-or-less a case by case basis. Sometimes sites bar there doors to certain browsers. LAUNCHcast, part of Yahoo! Music, is famous for this, only playing on IE in Windows and Netscape BC 27 (or something like that) on the Mac. Yahoo! still shuts doors to their new mail system that uses Ajax to anything other than Firefox, IE and SeaMonkey (old Mozilla).
This is what it looks like in Camino:

Here's a video if you want to learn a little bit more:
REFERENCES
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Scholarly Articles
Author Abstract:This paper aims to define users' information expectations as web technologies continue to improve in loading time and uninterrupted interface interactivity. Do web technologies like Ajax-or, more abstractly, a quicker fulfilling of user needs- change these needs, or do they merely fulfill preexisting expectations? Users navigated through a mock e-commerce site where each page that loads has a 50% chance of implementing Ajax technology, from functions of the shopping cart to expanding categories of products. Users were observed through eye tracking and measuring their pulse and respiratory effort. Questionnaires were administered before and after these tasks to assess their thoughts about the study. Qualitative and quatitative observation found users almost unanimously favored the Ajax functions over the non-Ajax. Users emphasized the usability concerns of switching to Ajax, especially concerning feedback. FULL TEXT (PDF)