The United States is to withdraw all its forces from Iraq by the end of next year. In that time, the roughly 50,000 American soldiers who remain will be trying to train Iraqi security forces to deal with the daily violence that still plagues the country.
There has been progress in recent years, and casualty figures are much lower than they were at the peak of the violence in 2006 and 2007.
But Iraq is still unstable and a stubborn insurgency continues to kill hundreds of people every month.
If you are looking for progress, go to Dora. It is a residential neighbourhood of Baghdad, its skyline dominated by the flare of a large oil refinery. Dora is a largely Sunni area.
For years, Salman Hassan, a Shia, had run a small ration shop, distributing sugar, flour and baby food to the locals, most of whom he knew by name.
But in 2006, sectarian violence drove him and his family from their home.
Until recently, Dora was one of Baghdad's most dangerous neighbourhoods, a no-go area for Shias and others, where shootings, kidnappings and killings were an everyday occurrence.
Now Salman says he feels safe here again. He has gone back to run his store, his customers popping in and chatting as if nothing had ever happened.
Dora is much safer than it was. But in Iraq, safety is always a relative concept. At the end of Salman's road, there is an armoured Humvee, specifically there to protect a Christian family after recent attacks.
Amid the signs of progress in Baghdad, there are unhealed wounds of the recent past.
Souad Abdullah was once one of Iraq's most famous singers. Today, she is a recluse, hiding in her small flat with the curtains drawn, working away at a sewing machine in the semi-darkness.
In February 2006 her son, Khalil, was snatched from the streets of Baghdad. He was taken in Sadr City, a vast suburb of Baghdad, which was then under the control of Shia militias.
As a Sunni, Khalil's chances of survival were slim. His kidnappers called Souad on the phone. They made her listen while they tortured him. She paid a ransom but they killed him anyway.
"I'm afraid just to step outside my flat, because they might shoot me," she says, even now. "I want an end to this nightmare. I'm exhausted."
This level of sectarian violence is rare in Iraq today. Things are getting better, a point that American officials never tire of making.
And in a sense, they are right. The question is, compared to what?
At the peak of the violence in 2006 and 2007, several thousand people a month were being killed. For the past 18 months that figure has dwindled to a fairly stable figure in the mid- to low-hundreds.
So, far fewer people are being killed than a few years ago; but it's still many more than before the invasion.
In almost any other country, this daily violence would be cause for a state of national emergency. In Iraq, it is called progress.
The Iraqi police look more like heavily-armed troops than bobbies-on-the-beat.
Recently, in central Baghdad, we watched a group of them come under fire from gunmen hidden in a pile of twisted scrap metal.
Cars sped off in a cloud of smoke, police bodyguards shot back, trying to protect their charge - a VIP of some sort.
This scene was an exercise, run by the American military.
But these men really do work at the sharp end of the profession. Instead of burglaries or anti-social behaviour, they still have shootings, bombings and kidnappings to deal with.
The Americans say their Iraqi counterparts have made huge progress in training over recent months. But there is still plenty of work to do.
One US trainer, a civilian working for a private company under contract to the Pentagon, who didn't want to give his name, said the new recruits made a number of crucial errors during the exercise.
"First mistake: they never closed the principal's (VIP's) door. So the sniper had full access to putting rounds inside the vehicle. So they're going to do it again, hopefully with better results."
The Iraqi police tried it again, and the American trainer pronounced himself more satisfied with their efforts. But in answer to the crucial question, whether the Iraqis will be ready to go it alone in a year's time, he answered simply:
"It will be very difficult, but we're going to try."
In private, many US commanders agree. The official line, though, is that the Iraqi security forces, which number in the hundreds of thousands, will be ready.
Lt Eric Giles was the soldier in charge of the American training unit that day.
"They are able to function, they are able to go out and prevent, they are able to react. And I think from what we're seeing right now from their leadership, they are well on their way to meeting that goal at the end of this coming year."
The US has made it clear that, if requested by the Iraqi government, it would be open to the possibility of retaining a certain number of troops in the country after their current mandate under the Status of Forces Agreement expires at the end of 2011.
But so far, the Iraqi government says it has no plans to ask the Americans to stay.
And with the anti-American cleric, Moqtada al-Sadr, set to play a significant role when the next government is formed, such a request is looking increasingly politically fraught.
In Baghdad, normal life continues. But it is not a normality most people would recognise.
It is a life lived in the spaces between concrete blast-walls, in segregated neighbourhoods, accessible only by invitation or special pass.
It is a city where military helicopters constantly buzz overhead, the streets clogged with traffic jams caused by hundreds of checkpoints searching for bombs and insurgents.
Life will certainly still be like this when the Americans pack up and leave at the end of next year. Many believe it will be like this for years to come.