I actually just learned about them after picking up Larry Ullman's PHP and MySQL book. Personally I'm not using them yet because, as is probably apparent, I'm new to all of this in general, and they're also not loaded in on my test machine (lazyness is not an acceptable excuse I know, but when you're learning... ).

Trying to load them in right now on my windows system, added the php_mysqli.dll, added libMySQL.dll to the path, and changed all my functions in a class to test it, restarted everything... and... not working. Page tries to load forever, so it's trying to do something because it won't die with an error. Hmmm... oh there it just loaded. Blank. Well then.
-m