There's concern for tens of thousands of civilians who remain trapped as Iraqi forces, under air cover from the international coalition, launch what Iraq calls 'the second phase' to take the IS stronghold.
The dawn offensive was launched on multiple fronts, as this Iraqi major reported.
"Our soldiers started their offensive at 5am today to retake Fallujah. They've advanced on several fronts against the extremists."
Under cover from the Iraqi air force and international coalition jets, ground forces pushed into Fallujah a week after beginning their offensive.
But they're facing fierce resistance.
Known as the city of mosques, Fallujah was taken by IS in January 2014, before the group's rapid spread across Iraq.
Up to 50,000 civilians are believed to be inside the city, trapped by the fighting and by IS, who are believed to be using them as human shields.
There are also reports of severe food shortages.
United States Colonel Derek Harvey was involved in the US-led attack on Fallujah in 2004 against the group's militant predecessor, al-Qaeda.
"What we're going to see is a transition. Eventually Mosul will fall, eventually Raqqa will fall. But you're going to have an ongoing contested very difficult fight for years and years, unless there's real progress. And we don't see the progress in Ramadi, or Tikrit, or Saladdin province to date, where the government - because of the political inability in the parliamentary fights, in the contesting for power and influence between Sunnis, Shia and Kurds -- in Baghdad there's no progress at all. So this is going to be a struggle for, I'm afraid, many more years."
But some analysts are concerned over the ultimate goals of some involved in the Fallujah offensive.
Michael Pregent is a Middle East analyst who specialises in counter-insurgency.
"If you look at the public relations photos that are coming out of Fallujah, you have women and children being given water bottles by Shia militiamen. But where are the men? The men are not there. What they do is they take the men, and they put them somewhere else and a militia man decides -- is he Daesh? or is he a collaborator? The punishment is the same. So this is not a counter-insurgency strategy, and this is nothing that the United States should be taking part in because it is indiscriminate targeting, it is giving primacy to Iranian-backed Shia militias and it's not going to win over the Sunni population that's needed to fight ISIS."
This imam, originally from Fallujah, is now living in a camp for internally displaced people in eastern Iraq.
"As for the acts of revenge, we are urging the Iraqi and American governments who approved this operation to make sure that the people of Fallujah do not get killed and the city of Fallujah doesn't get destroyed. There are people who we do not want to name who want to come to take revenge. They are claiming that the people there did this and that. That they destroyed the country."
