If Iraq's army succeeds in recapturing Fallujah, this will amount to its biggest victory over Isil since the conflict began. More than any other Iraqi city, Fallujah served as a jihadist heartland.
This forbidding jumble of mosques and flat-roofed homes on the banks of the Euphrates was the first urban centre in Iraq to fall under the black flag of the Islamic State of Iraq and the Levant (Isil) as long ago as January 2014.
Other Isil conquests - notably the city of Mosul - have mixed populations that once included Kurds, Yazidis, Christians and Shias - or at least they did until the terrorists carried out their campaigns of expulsion and massacre.
But Fallujah is inhabited almost entirely by Sunni Arabs: its 300,000 people were regarded as natural subjects of Isil's "caliphate". If the jihadists lose their grip on Fallujah, this will be their biggest setback since the lightning offensive of 2014, when they swept down the Tigris and Euphrates valleys and captured a swathe of Iraq.
Many of those conquests have now slipped from Isil's grasp. In the last year, the jihadists have lost almost half of the territory they once controlled in Iraq; the number of "foreign fighters" arriving to replenish their ranks, meanwhile, has plunged by 90 per cent.
If they lose Fallujah, then Mosul will be the only big urban centre still under Isil's flag in Iraq.
The Iraqi army that was routed with such ease only two years ago has shown its ability to achieve real victories, albeit with the help of Western air strikes and powerful militias.
So runs the good news. But there are plenty of reasons to feel unease over what comes next.
First of all, Shia militias - armed and, in large measure, controlled by Iran - still provide the spear-point of the forces loyal to the Baghdad government.
Whether the overwhelmingly Sunni population of Fallujah will regard the arrival of Shia soldiers as a genuine "liberation" remains to be seen.
The next objective of Iraq's counter-offensive will be to drive Isil from Mosul. But this will be a much tougher task, partly because Mosul is five times bigger than Fallujah - with a population of 1.5 million compared with 300,000 - and also because all the evidence suggests the terrorists are preparing extraordinary measures to defend the last big prize within their grasp.
Moreover, even if Isil loses every city and all the territory in its domain, experience suggests that it will not be eradicated.
Instead, the jihadists will switch tactics and adopt guerrilla warfare and urban terrorism, carrying out hit-and-run attacks. The loss of Fallujah will be a significant defeat - but not nemesis for Isil.