All this while, Opera has mainly targetted higher end phones for their mobile browser. Today, they released Opera Mini. Opera Mini is a stripped down version of Opera which will run on lower end phones. It's written in Java, so the phone needs Java support. Instead of doing all the processing on the client (like they do in their full mobile browser), they have a proxy server that converts the data into a format suitable for the phone, and the client just renders that.
This is all VERY similar to the initial WAP idea, with one major difference: while the original WAP spec needed content developers to develop in WML, with Opera Mini you can visit the very same HTML sites that you do on your desktop. This is a big difference. One of the main reasons that WAP has not really caught on is because of the lack of quality mobile content (remember, you can't view HTML pages). The WAP 2 spec rectifies this by adding support for XHTML and CSS, but all the processing is done by the client. Opera have combined both ideas in Opera Mini.
There are still a number of potential pitfalls. Another reason why mobile browsing hasn't caught on was because of slow and expensive bandwidth. Yet another reason has been difficulty in reading on a small screen and clunky input via a telephone keypad. Neither of these have been solved. Opera uses compression and small screen rendering (which modifies the page to accomodate a small screen) to try to solve these problems, but the solutions have only been okay. I'd love to try it out to see how it scores on these points.
Opera Mini is only available in Norway at the moment (no idea why). Can't wait to try it out when it releases here.