They edge towards the city limits, using artillery and airstrikes to soften up the terror group's defenses. ISIS retaliates with suicide bombs, exploits its tunnel networks and activates sleeper cells elsewhere in the city.
A long battle of attrition is underway, with some 750,000 civilians caught in the middle. For the Iraqi army and government, the prize is clearing ISIS from the last city it holds in Iraq.
The battle for western Mosul is likely to be tougher than that for the eastern half of the city, which took well over two months. Satellite imagery and witness accounts indicate that ISIS' defenses are thicker here, and the warren of alleys in the old city is impenetrable to armored vehicles.
On the upside, Iraqi special forces gained hard-won experience in the east. One sergeant in the Counter Terrorism Force told CNN last month that his unit had stopped using vehicles and had pushed forward at night on foot, frequently surprising ISIS fighters.
In the initial stage of this latest offensive, the Iraqi Federal Police and the 9th Armored Division have begun shelling areas around Mosul's airport, to the south of the city, ahead of a ground advance. ISIS has heavily fortified this area with road blocks and berms, and long ago rendered the airport runway unusable with trenches. Iraqi military officials said Tuesday that the first target, a hill to the south which overlooks the airport, had been taken.
In support, US airstrikes have targeted ISIS operations inside the city, most notably with a bombardment of its command headquarters in the five-story Bab Sinjar building on February 17. The coalition reported heavy airstrikes Monday against ISIS command centers and more than a dozen of its mortar units.
There is one major difference to this phase of the battle. When they were in eastern Mosul, ISIS fighters had the option of dropping back to western Mosul.
Now they are bottled up in a small pocket of territory, with escape routes across the desert and toward Syria blocked off by Iraqi paramilitaries. The vast majority will have to choose between death and surrender -- which will only make the battle even harder.
What about the civilians?
There are also fewer choices for the civilians. All the bridges linking east and west Mosul have been destroyed. Escaping to the south, through the fighting, would be perilous, but basic supplies are running short. The UN Office for the Coordination of Humanitarian Affairs (OCHA) says "available food and fuel supplies continue to dwindle, with residents resorting to burning furniture and rubbish to keep warm.
"Food and fuel supplies are dwindling, markets and shops have closed, running water is scarce and electricity in many neighborhoods is either intermittent or cut off," OCHA said this week.
The exodus from eastern Mosul was substantial (about 180,000 at its peak) but manageable, with well-established camps beyond the city limits. A prolonged fight in the west would have worse consequences. At present, OCHA says, there is space prepared for some 60,000 displaced people.
Do the Iraqis have enough troops?
To root ISIS out of western Mosul, the Iraqi military has had to deploy many of the elite units that took the eastern neighborhoods. The risk is that 'holding forces' left behind are less experienced and less disciplined, according to some western observers. A CNN team in eastern Mosul last month found the brittle mood among a civilian population that was beginning to return home but wary of the fragile security situation.
There has already been a spate of suicide bombs in eastern Mosul since ISIS fighters were driven back across the River Tigris. Eleven people were killed in one attack on a restaurant on February 10. It is a large area to police and Iraqi officers told CNN last month that sleeper cells were a constant worry. The worst-case scenario would be for clashes to erupt again in the east, forcing Iraqi units to fight on two fronts at once.
What comes next?
The bigger picture, once this battle is won, is about reconstruction and reconciliation. Large tracts of eastern Mosul have been devastated. Burned-out vehicles litter the streets, thousands of homes are rubble, much of the infrastructure is ruined. Services and security need to be restored if people are to be persuaded to stay -- but the price tag is likely in the billions. And that's before the cost of the battle for western Mosul is considered.
Nor is there yet any agreement on how to govern Mosul, an ethnic and sectarian fault-line where Sunni, Kurdish, Shabak, Christian and Turkmen groups -- often themselves divided -- will jockey for influence in the vacuum left by ISIS' departure. Kurdish Peshmerga forces have already built a massive berm in a unilateral attempt to draw a new border for their region.
Kurdish officials are apprehensive that once Mosul has fallen, US interest in the region will wither, though senior figures in the new administration have pledged that the "strategic US-Iraq relationship" endures.
Throughout 2016, US diplomatic stamina was critical in building and holding together the fractious coalition of the Kurdish Regional and Iraqi governments, as well as the various militias that want a say in how this part of Nineveh province is run.
Analyst Michael Knights, who has long experience working with the Iraqi military, says
continued US involvement is critical. "US forces should commit to at least three more years of extraordinary security cooperation," to solidify the hard-won gains in Mosul and elsewhere."
Will this be the end of ISIS in Iraq?
The liberation of Mosul just might offer a template for sharing power and resources in Iraq -- but the experience of the past 14 years is not encouraging. Sectarianism, corruption and more recently the fall in the price of oil have all hobbled efforts to put Iraq back on its feet. Even if ISIS is decisively beaten in Mosul, its deep roots in Iraq will not have been eradicated. It will try to revert to what it was -- an insurgency living among Sunni populations throughout northern Iraq, hiding out in areas like the sparsely-populated Hamrin mountains.
In areas of Diyala province and around the town of Tikrit, ISIS is already showing signs of renewed life. Earlier this month, the Governor of Salahudin province appealed for help from Baghdad after a spike in attacks. The Institute for the Study of War -- which monitors the security situation across Iraq -- says ISIS is "returning to traditional ... terror tactics outside of its efforts to govern and hold cities."
One Kurdish intelligence official, Lahur Talabani, told Reuters last week that even if ISIS evaporates "another group will pop up under a different name, a different scale."
"These next few years will be very difficult for us, politically," Talabani said
Nowhere is that more true than in Mosul, Iraq's second largest city. Rasha al Aqeedi, one of the many Mosulawi in exile, says
it would be a tragic mistake for people to think "there is only one kind of resident in Mosul, one kind of Muslim, or one kind of anything else."
"The place is just not that simple, and missing the details is bound to end in tears for everyone."