American troops have arrested over a hundred Arabs trying to cross the Syrian border to join the fighting against American troops.
The al Sadr Shia militia that have taken control of towns and neighborhoods from Baghdad to Basra. These militias are not well organized, nor do they have very effective leadership. American and coalition troops are arresting and killing the Sadr men who are armed and resisting. The Sadr followers have little military training (or if they do, it doesn't show) and poor organization. Sadr is trying to get more Shia to join the fight. But this becomes more difficult as more Iraqi fighters are killed fighting the better armed and organized coalition troops.
The Iraqi police and security troops have been a disappointment. With few exceptions, they refused to oppose armed Sunni Arabs in Fallujah or Shia areas in the south. This was expected from the security troops, who are basically security guards. The police, although they received training, were recruited locally. So if a local strong guy gathers together enough armed men, the local cops will back off. This is a vestige of the Saddam era, where the police were basically security guards, which the heavy duty terrorism was performed by various secret police, pro-Saddam militias and intelligence organizations. Coalition troops are able to use the security troops and police and the current fighting, putting the Iraqi forces in charge of security in areas that have been pacified.
Fighting continued in Fallujah, with the marines holding nearly half the city, and inflicting over a hundred casualties on the armed Iraqis. The marines are using a combination of tanks, aircraft and infantry to advance against the Iraqis defending from the tightly packed, low rise (one or two story) housing that covers most of the city. There are numerous different groups resisting the marines, so there is no coordinated resistance. The criminal gangs appear to be the best organized. The gangs of Fallujah, like many Sunni Arab criminal organizations, proved resistant to Saddam's attempts to destroy them, so Saddam made a deal with the gangs, and got a cut of their loot. The former Saddam military and secret police people have formed anti-American (and sometimes criminal gangs, which causes tension with the existing gangs.) There are also groups of Arab nationalists (whose philosophy seems to be "better to be a slave under another Arab than to be free through the efforts of a non-Arab) and Islamic radicals. This lack of centralized organization makes it harder for the marines, as killing off one group does not have an immediate effect on the others. However, killing the resisting Iraqis does have an effect on others. The number of Iraqi gunmen is diminishing as Iraqis note that the marines kill all who fight them, and the marines are not taking nearly as many casualties as the Iraqis.
The annual rotation of new American troops relieving those who have already served a year has been halted, and experienced units held until the current unrest in Fallujah and Shia areas is over.