The Iraqi Army is hustling to get ready to deal with Iran, by the time the last 50,000 U.S. troops leave at the end of the year. Increased oil production, and oil prices, has made it possible to recruit more troops, and equip more combat divisions. Particularly noteworthy is the creation of Chemical Defense Regiments, with the goal of one of these units being assigned to each combat division over the next few years. The only neighbor known to have chemical weapons is Iran. Iraqi diplomats spend a lot of time trying to improve relationships with Iran, but just in case things go south, the Iraqi military is preparing for the worst.
While Iraq has sought to obtain a lot of American weapons, particularly tanks, artillery and combat aircraft, it's been easier, and faster, to get Russian type gear from Russia or East European nations. A lot of this stuff is newly made, but most of it is Cold War surplus. These vehicles and artillery are cheap, a lot of older Iraqis are familiar with them, and they are as good as anything the Iranians have.
The Iraqi ground forces currently have nearly 200 infantry and tank battalions, organized into over 70 brigades and 17 divisions. There are a lot of independent brigades, and divisions are still waiting to receive artillery and armored vehicles and support units. Meanwhile, troops spend a lot of time performing security tasks, to aid the effort to track down the few remaining Sunni Arab terrorists.
By the end of the year, the army will have about 230,000 troops. They will not be as well as equipped as during Saddam Hussein's tenure (1960s-2003), but they are better trained. This is important, because Iraqi troops have long been the least effective in the Arab world, largely because of poor leadership. The war with Iran in the 1980s changed that, but Saddam purged most of the competent new leaders, soon after, as he feared they would lead a coup against his disastrous rule (he was probably right.)
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 that, the Sunni Arabs loyal to Saddam (and Sunni Arab rule) fought a four year terror campaign. One response was the army forming the best troops into special "intervention" units. This resulted in an army organization consisting of one "Intervention Corps" and three other corps of lesser quality. Most divisions have four brigades, and a total strength of about 12,000-15,000 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."
Another independent security forces is the 1st and 2nd Presidential Brigades (for guarding senior officials), which is controlled by the armed forces headquarters.
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 serve as mountain divisions, but lack a lot of heavy weapons (tanks and artillery).
The Central Corps is the area around Baghdad, and the thinly populated Anbar Province to the west. This corps has two motorized divisions, one infantry division and one commando division.
The Southern Corps has three infantry divisions, with another infantry division planned. One of the existing divisions is motorized and another is designated a commando division,
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 50,000 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 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, but there are still a lot of bad habits (corruption, especially) that degrade combat effectiveness.