Implementing asynchronous callbacks in asp.Net 4

Internet application development can be seen as the a stateless client-server programming using a thin client.In case that we don't like this approach, we have several methods to change it.
The cause of such adaptations most often stems from specific business needs and rules.

Sometimes, software engineers want to make the client a bit more thick. They usually do this by adding code to the client side, i.e. JavaScript, vb-script, etc. Other times, want to make UI more... feasible. By 'feasible' I mean that it is not necessary to post-back a whole page just for a very simple calculation. One solution to this issue is to put simple calculations to the client side (using JavaScript). But again, what if the operands are members of  some more generic object that cannot be transferred to the client, such as a large database table? Is then the post-back a one-way solution? Well, no. The answer can be called AJAX or in other words (a more MS oriented ones) Asynchronous Callbacks.