(CNN) This week, the Iraqi military announced that its forces had reached the Tigris River for the first time in the battle for the key city of Mosul.

The advance is seen as a significant moment in the three-month campaign to recapture the city. Since October, a coalition of Iraqi-led forces including the Iraqi army, counter-terrorism forces, federal police, Kurdish Peshmerga fighters and Shiite-led paramilitaries have pushed to end ISIS' brutal rule in Mosul.

The city remains the last major Iraqi stronghold of ISIS after the militant group seized control in 2014.

The operation to liberate Mosul is taking longer than expected and the suffering of civilians there is only increasing.

How significant are the recent advances in Mosul?

They are very significant. Toward the end of November, it seemed that the Iraqi Special Forces were getting bogged down in eastern Mosul, hit by countless suicide bombs as well as mortar fire from areas where civilians were present. There was a deliberate pause toward the end of December to reassess.

More forces, including the Iraqi Federal Police, were brought to the eastern side. The relaunch of the campaign has featured rapid assaults to punch through ISIS resistance in neighborhoods on the right bank of the Tigris. By January 8, Iraqi forces had reached at least one stretch of the river bank and now control about two-thirds of eastern Mosul.

"In the second phase of Mosul operations, we have used new methods in fighting ISIS militants," Lt. Gen. Abdul Wahab al-Saadi, commander of the liberation of the city, told CNN on Wednesday.

"The most effective method was the night raids conducted by Iraqi troops against ISIS headquarters and positions in eastern Mosul."

It may be that ISIS calculated there was little to be gained by further fierce resistance in the east, given that the bridges across the Tigris were unusable

A picture shows the Fourth Bridge over the Tigris River connecting eastern and western Mosul during an ongoing military operation against the Islamic State (IS) group on January 10, 2017.

There is also the possibility that it's running out of suicide bombers; several of those recently eulogized were teenagers. But there may be weeks of fighting before ISIS relinquishes its foothold in eastern Mosul. There are still tens of thousands of civilians there, which makes offensive operations much harder.

Are there a lot of territories left under ISIS control?

All of western Mosul as well as pockets of resistance in the city's environs. Western Mosul, according to satellite imagery and the accounts of former residents, is going to be a much tougher proposition.

The older part of the city has warrens of alleys that are impassable to military vehicles. ISIS has dedicated much of its defensive preparations to this area; Iraqi Security Forces will not be able to attack across the river because all five bridges are heavily damaged, so the offensive will have to come from the south and west.

A Google Earth satellite image taken before the operation captures Mosul's five bridges spanning the Tigris River.

According to the latest assessment from the Institute for the Study of War, the army "will likely pause before an operation launches to cross the river in order to regroup and plan for the likely stiff ISIS resistance on the western bank."

Even when Mosul is finally cleared -- and that could take until the spring -- ISIS is likely to be able to continue to launch suicide attacks in much of Iraq, including Baghdad

Staff General Taleb Shegati al-Kenani (C), top commander of the Counter-Terrorism Service, studies a map with his team of officers in Mosul's Al-Zahraa neighbourhood on January 7, 2017.

There are signs that ISIS are regenerating an underground presence in places where it has lost territorial control, such as Diyala. And it still controls some towns in the west of Iraq. But the loss of Mosul would essentially leave the so-called Caliphate a string of towns under pressure -- from Raqqa in Syria westward.

Why is it taking so long for the army and allied groups to recapture Mosul?

Urban warfare, especially in the midst of hundreds of thousands of civilians, is the most difficult there is. Tikrit, Ramadi, Fallujah were all tough, and they are much smaller than Mosul. The forces tasked with retaking Mosul have largely been the spearhead in a two-year war of attrition against ISIS.

They have suffered losses of experienced combat troops and equipment. Many of the units involved have little sense of Mosul's geography. They have learned on the job. And in Mosul, they don't have the direct assistance of the Shia-dominated paramilitary units that were an important factor elsewhere.

Members of the Iraqi special forces Counter Terrorism Service (CTS) clear a building as they advance in Mosul's eastern al-Karamah neighbourhood on January 2, 2017, during an ongoing military operation against Islamic State (IS) group jihadists.

Are the US-led airstrikes helping?

Yes. As intelligence and co-ordination have improved, so has targeting. Since the offensive against Mosul proper began early in November, there have been hundreds of coalition airstrikes against ISIS positions.

Al-Saadi told CNN that the Iraqi Air Force and US-led coalition have increased airstrikes on ISIS-held areas of eastern Mosul.

"Many ISIS militants were killed, several ISIS headquarters were destroyed, and ISIS leadership in eastern Mosul has started to collapse," al-Saadi said from inside Mosul.

On Monday alone, according to the coalition , airpower engaged four ISIS tactical units; destroyed seven ISIS-held buildings, four vehicle suicide bombs and a factory that makes them, and damaged 18 ISIS supply routes. That's a typical day. But the terrorists' use of tunnels and mobile mortars, their ability to hide among civilians in abandoned properties, has made the use of airpower more challenging.

It is a slow, grinding process but as Colonel John Dorrian, the coalition spokesman, puts it: "Every day the Iraqi Security Forces go forward and every day the enemy goes backward or underground." The latest offensive has been helped by the presence of some 450 US and coalition personnel within the city limits, offering advice and support.

Soldiers of Iraqi Army and Hashd al-Shaabi militias arrive at Saleh Village after retaking of Khalid, Saleh and Zanawer Villages of Qayyarah Town from Daesh terrorists during the operation to retake Iraq's Mosul from Daesh terrorists, in Mosul, Iraq on October 20, 2016.

What about the civilians living in both parts of Mosul?

The latest UN data is that 135,000 people have been displaced by the battle for Mosul. Many more have decided to take shelter in place, not least because ISIS frequently fires on civilians who try to leave. UN agencies note that, in one week alone, nearly 700 people in the east were taken to hospital with trauma injuries.

Those who stayed have had intermittent power and water at best, and dwindling stocks of food. As soon as their neighborhoods are liberated, large lines form for food aid and basic medical treatment. The United Nations and NGOs would much rather people stay in their homes because camps are already near to capacity.

Iraqi civilians fleeing their neighbourhoods due to the ongoing fighting with Islamic State (IS) group jihadists arrive to the northern edge of al-Mithaq neighbourhood in southeastern Mosul, on January 4, 2017.

On Wednesday, Lt. Gen. Raed Shakir Jawdat, commander of the federal police force, announced that ISIS militants were forcing people to leave their homes, herding them behind enemy lines and using them as human shields to stymie advancing Iraqi troops.

Back in October, Lise Grande, the UN Humanitarian Coordinator for Iraq, said that if more than 150,000 people were forced to flee Mosul "there isn't an institution in the world that could cope with that scale of movement."

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The most hopeful sign is that markets and more organized relief efforts are beginning to bring a semblance of normality to recently liberated districts. Last week alone, 50,000 people received food and hygiene-related aid, according to a UN report on humanitarian response.

The situation in western Mosul is much worse, with shortages of basic goods amid siege-like conditions. "Bakeries are not functioning in many areas and residents are not allowed to use generators, even if they have fuel to power them," says the latest UN assessment. And for the people there, the prospect of liberation is likely months away.