The Iraqi Army has come a long way since 2003, when the old, Sunni Arab dominated force was disbanded, and a new one, loyal to a democratic government, and led by newly recruited and trained officers, was built from scratch. Because of the Sunni Arabs loyal to Saddam (and Sunni Arab rule) fought a four year terror campaign, while the army was forming, the best troops were formed into special "intervention" units. This resulted in an army organization consisting of one "Intervention Corps" and three other corps of lesser quality. Total manpower is about 250,000 troops. Most divisions have four brigades, and a total strength of about 12,000 troops.
The 1st Intervention Corps consists of the two motorized, one infantry and one armored divisions. One of the motorized corps is the also known as the Reaction Force Division. This is considered the most effective division in the army, and one to be used for the most difficult situations. Think of this corps as the new "Republican Guard."
The other three corps are named after the part of the country they are based in.
The Northern Corps has two motorized divisions and an infantry division. Two divisions of Kurdish troops will, eventually, come under army control as mountain divisions.
The Central Corps is the area around Baghdad, and the thinly populated Anbar Province to the west. This corps as the 1st and 2nd Presidential Brigades (for guarding senior officials) The Baghdad (56th) Brigade (for assisting with security in the city), two motorized divisions, one infantry division and one commando division.
The Southern Corps has three motorized divisions, with an infantry division being formed.
There are other security forces, mainly four divisions of Federal Police, the Counter-Terror Command (with seven commando battalions and support troops), the Border Police and half dozen battalions worth of "Emergency Police" (SWAT, riot control) distributed around the country. These other security forces are nearly as large as the army, but are not as heavily armed, or trained for heavy combat.
The navy is currently, basically a coast guard. The air force consists of about a hundred transports, helicopters and recon aircraft. The 140,000 U.S. troops are mainly deployed in bases around Baghdad, and northern cities.
Even the army does not have a lot of heavy weapons. There are only about 300 old T-72 tanks, and lots of newer armored hummers. Thousands of new armored vehicles are on order. Compared to Saddam's force, the NCOs and officers (mostly from the Shia Arab majority), have less time in uniform, but are better trained. The Iraqis have learned a lot about fighting from their American mentors. For a long time, Iraqis were considered the most ineffective military forces in the region. Not so much, not anymore.