The assault on Fallujah has begun. For analysis of events visit Adventures With Chester:
The New York Times is reporting that the hospital was seized by the 36th Iraqi Commando Brigade in conjunction with US Special Forces. This is important in that it shows the high initial involvement of Iraqi National Forces.
NYTimes also reporting (same article) that thousands of Marines are moving from their base to a point north of Fallujah. Their base is likely Al-Taqqadam airfield, and they are likely moving across the western bridge they just seized. This makes sense; a large armored force will now be positioned on the eastern side of the Euphrates, and north of the city. That means it can either rapidly move along the highway toward Baghdad in pursuit of insurgents, or it can use the same highways to position itself on three different sides of the city, with the Euphrates on the fourth.
There's much more at his site.