US troops faced some determined resistance
The BBC's Gavin Hewitt is with American forces on the south-western outskirts of Baghdad. Here he describes the push they made into Baghdad.
It was yesterday, Sunday, that the armoured unit from the 3rd infantry division that I'm travelling with pushed down the main highway from the west towards the centre of Baghdad.
As it pushed down that highway it did meet some resistance. For a while it seemed very determined resistance - some artillery was fired by the Iraqis.
Then the armoured unit pushed off the main highway into a military area. The Iraqis again put up some resistance there too but they lost a large number of tanks and armoured personnel carriers.
I saw about 12 or 15 burning in the past 24 hours just from the one area.
At the same time, some civilians who were driving nearby during these fierce fire-fights got caught up in this battle and afterwards we saw Iraqi bodies - soldiers and also civilians - lying beside the road.
Fierce fights continued overnight but they tended to involve disorganised bands of Iraqi soldiers.
There didn't seem to be any great plan for the defence of Baghdad.
Some of that has subsided today, although skirmishes continue.
The battle is by no means over
At the position where I am, the Iraq army left about an hour ago but the civilians are still cowering.
There are between 30 and 40 of them very close to where I am, holding up white flags just hoping that some of this firing, which has been intense for periods, might subside.
There's no question that the Americans are driving the Iraqi militia from the city, but it is at a cost to the civilian population.
And this part of the city is certainly not yet secure. It's a very edgy situation as far as the Americans are concerned.
But the Iraqis no longer control it. Many of them have just faded away, particularly the soldiers, and I have seen uniforms just thrown to the ground.
The organised resistance is small. I don't think there is now an Iraqi plan for the defence of Baghdad, it's ad hoc, sporadic - but that can also be very dangerous.
I think the Americans are on alert the whole time, expecting attacks, and I think it will take some days before those kinds of attacks disappear.