Facebook is actively working on a new advanced application for iPhone OS 3.0.  Facebook software engineer Joe Hewitt wrote a post stating that he is about 98% done with it and even listed the features that will be included:

1. The “new” News Feed
2. Like
3. Events (including the ability to RSVP)
4. Notes
5. Pages
6. Create new photo albums
7. Upload photos to any album
8. Zoom into photos
9. Easier photo tagging
10. Profile Pictures albums
11. A new home screen for easy access to all your stuff, search, and notifications
12. Add your favorite profiles and pages to the home screen
13. Better Notifications (they link to the comments so you can reply)
14. Quickly call or text people right from the Friends page
15. Messages you are typing will be restored if you quit or are interrupted by a phone call

Push is not ready as of yet, but Facebook is working on it.  The 3.0 version may not have it, but the 3.1 version will most likely have it.

[via Facebook Blog]