Counting the number of clicks without redirect?

I see some directories that count the number of clicks on a link without having a redirect page. How is that?

 

The link could have a Javascript event that counts the clicks, or it could redirect to a PHP page that has a header redirect to the new page (therefore seemingly instant).

 

With javascript how they save the result?

And about the other the whole point is not to have a redirect because people wouldn't be interested in adding links.

 

AJAX could send the click event to a php file that stores it in the database.

 

Thanks, this seems to be what I need.