Families in the city, which is under Islamic State control, have been told to flee or raise a white flag.
There had been weeks of 'shaping operations' as villages were taken to the south and north of Fallujah.
The city of 100,000 people had been besieged for months and those who could escape spoke of hunger, no medical supplies, and fear.
Then at the weekend the 16,000 families who make up a population that has lived under the control of the so called Islamic State for two years were told to flee.
Those unable to leave should raise a white flag. Above all, they should stay away from militant fighters.
The bombs began to rain down on the already battered city on Monday.
Carefully targeted, no doubt, by coalition aircraft while infantry from a smorgasbord of fighting units gathered on the outskirts of this city that, for decades, has been synonymous with defiance – even under Saddam Hussein.
No one knows how many fighters remain in the city. But there is an assumption they will stay to fight and not flee as they did, in the end, from Ramadi.
If they choose to fight the battle will be long, and bloody, and may well not have been worth fighting at all.
Fallujah is Sunni.
So-called IS is entirely Sunni.
And the people of Fallujah have every reason to be deeply suspicious of the Shi'a dominated central government.
Sunnis who had fought al Qaeda in the later part of the last decade had been promised a role in a new Iraqi army and genuine political power in the centre. They got neither.
Indeed, Sunnis were purged from the military and corruption replaced professional units with ghost soldiers that vanished in the face of the 'Caliphate's' onslaught two years ago.
But there is no natural support for the extreme brutality of the Caliphate.
Its followers' addiction to ultra-violence and belief that they are living in the End of Times, is seen to be as creepy as it grotesque by most Sunni believers.
The militants will know, though, the greater the civilian death toll the greater the chances that Sunnis elsewhere in Iraq will rally to their black flag – if only out of sectarian solidarity.
They know that Fallujah is a test bed for the far greater prize of Mosul, Iraq's second largest city and the biggest under IS control.
Shaping operations have begun there, too.
But only an uprising from the two million people within it against the Islamist death cult will bring it back into government hands.
And that will not happen if there is the bloodbath that the Caliphate will try so hard to deliver in Fallujah.
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