US and Iraqi forces have launched a full-scale ground assault on the rebel-held Iraqi city of Falluja.
BBC correspondents have been considering the tactics and significance of the operation.
Q: Why Falluja?
Falluja has long been a thorn in the side of US-led coalition forces. It has become a massive security problem since rebels established control following a stand-off in April and the city became a no-go area for the US and its allies.
US troops, supported by forces from the interim Iraqi government, hope to drive a stake through the heart of the insurgency, opening the way for elections to take place across the country in January.
Q: What methods are the US-led forces using?
This assault on Falluja has differed from that in April, when the US relied mainly on aerial bombardment. This time, US and Iraqi forces have gone in on the ground.
Over the past few months and weeks, the US battered Falluja from the skies in readiness for the ground assault. The multinational force has redeployed forces within the country, including moving 900 British soldiers north, to release US units in preparation for renewed operations.
US marines have been training in urban warfare
US troops have been moving through the city street by street, backed up by helicopters, rockets, tank fire and huge bombs. They have sunk all the boats in the reeds along the river to prevent their use by suicide bombers.
As loudspeakers in mosques called on fighters to defend Falluja, the US replied with heavy metal music and sirens played over a deafening megaphone.
The troops also have sophisticated technology at their disposal, including the Miclic mine-clearing system - a rocket-propelled 100m (300ft) length of rope encased in explosive that clears a path through minefields and blows up roadside bombs.
Other gadgetry includes the PakBot - a remote-controlled robot running on tank tracks that can go into houses, climb stairs and send back images.
Q: How successful is the operation so far?
US commanders say they are surprised at how quickly they have made progress and that they are ahead of the battle plan.
They say they expected heavy resistance on the outskirts, scattered bands throughout Falluja and then a hard core at the very end.
On the second full day of the assault, US troops had already reached the centre of the city, where they reported encountering heavy resistance.
The US military said American and Iraqi troops had re-taken key buildings, including the mayor's office,
meeting only "small pockets of fighters".
Q: And what about the insurgents?
The insurgents are said to have their strongholds in the northern Jolan district of the city, a warren of narrow streets that is a haven for rebels.
The insurgents may have at least as good intelligence as the US-led forces. They know the area better, and may have infiltrators among the translators of liaison personnel operating with the US and Iraqi government units.
Their aim is to drag US-led forces into a protracted battle on the ground and inflict as many casualties as possible.
Snipers have been firing at American and Iraqi forces from mosque minarets and apartment buildings.
Q: What are the risks to the civilians?
Between 30,000 and 50,000 civilian residents are thought to remain in Falluja - some figures estimates put the figure even higher.
The normal population of the city is put at about 250,000, although estimates vary wildly.
UN Secretary General Kofi Annan has expressed particular concern over civilians, saying that the assault risks dividing Iraq still further, not aiding elections in January. Leading Sunni politician Adnan Pachachi has warned that any excessive force will fuel hatred and resentment.
US Defence Secretary Donald Rumsfeld has insisted he does not expect there to be large numbers of civilian casualties at the hands of US forces.
He said Falluja residents have been warned to stay out of the line of fire, by staying off the streets and away from windows.
The BBC's Paul Wood, who is embedded with US troops in Falluja, says marines are carrying out what they describe as "precision attacks" against specific targets, to minimise civilian casualties.
However, he says the use of heavy weapons on poorly constructed houses can result in "secondary" damage beyond the building that is the target of the attack.
Despite the skill and the best efforts of the marines, "we are going to see civilian casualties", our correspondent says.
Q: What are the risks to the US and Iraqi forces?
They face a serious challenge in retaking Falluja. US commanders are confident they can win a conventional battle, but that is not the fight they face.
Urban warfare is the most dangerous form of fighting the military is ever involved in. On the street, the attackers are vulnerable - in their hideaways, the defenders are well protected. And each time an area is taken, it has to be kept secure until the whole battle for the city is over.
The Americans have done some street fighting in Iraq already - and train heavily at specially-built model towns - but it is not something they are really experienced at.
They may take lessons from Israeli troops who have developed special street-fighting techniques, such as moving from building to building by blowing a small hole in the adjoining wall, rather than going back into the open.
Q: What happens if and when the city falls?
If the US tactics work and they take Falluja, problems may still remain ahead.
A key question is whether there are enough effective Iraqi forces not only to take on a significant role in the offensive, but also to hold Falluja once the major fighting is over.
Indeed, what happens after the actual fighting, in terms of providing aid, reconstruction, and political support in Falluja, is at least as critical as the military part of the strategy.
The hope among US and Iraqi government strategists is that the insurgents will at last be on the run and that the tide of insurgency across Iraq will be turned. The fear is that the insurgents will gain more support - that they will be dispersed but will not disappear.
Q: What about political fallout from the offensive?
The US-led operation has already had an impact on Iraq's fragile political system.
The country's largest Sunni-led political party, the Iraqi Islamic Party, has pulled out of the interim government in protest at the Falluja assault.
The party, which was the only Sunni party in the government, has also said it will boycott the elections.
Sunnis represent a quarter of the Iraqi population and their refusal to take part in the political process would be a severe embarrassment for the US, according to political analysts.