Mosul was the capital of the Daesh or the Islamic state. This was the place where the ISIS chief Abu Baghdadi crowned himself the Caliph. The Iraqi Army has been planning an offensive to recapture the city since 2015. The army could only muster courage in October 2016 for the assault. In the battle, the Army failed to make much headway in recapturing the City. The battle dragged on for months and perhaps the Iraqi Army would never have captured Mosul but for the support by the US Air Force and Navy. The ISIS had no air cover. Control of the sky was with the US Air Force.
This is reported by the NY Times.
Victory of air power
Giulio Douhet's theory that Air Power as a decisive factor in winning a war was never truer than in the battle for Mosul. The US Air Force and Navy carried out a relentless bombing of ISIS positions. This relentless bombardment paved the way for the Iraqi Army to enter Mosul. They were also assisted by US special forces which operated alongside. In case the Army had not received support the possibility of recapturing Mosul was minimal.The Last stronghold of the Islamic State the famous mosque was destroyed by them before they retreated. The Iraqi Army's claim that they had won the battle and the ISIS are finished is just bragging.The US Command has cautioned against making such statements and pointed out that the Islamic State still remained in control of vast areas of Iraq and Syria.
They are also holding out in some pockets of Mosul. Overall the capture of Mosul is not because of the efficiency of the Iraqi Army but because of Air Support by the US Air Force and Navy as well as the special forces which fought along with the Baghdad Army.
The US will have to keep a permanent presence in Iraq.In case the US forces are withdrawn and the Iraqi Army has no air support the chances that it will lose to the Isis fighters is within the realm of possibility.
The Iraqi Army did not distinguish itself 2 years back when it lost 80% of Iraq to the ISIS led by Baghdadi. it was a crushing defeat.
ISIS not finished
The question that begets an answer is how long will the US keep on propping the Iraqi army and the Baghdad government. The ISIS may have lost Mosul but they have not been wiped out.
They still have tremendous propensity to wage war in other theaters of the world. In hindsight, one can see that action of George Bush in removing Saddam Hussein who had kept the Islamic extremists at bay was a great mistake. It appears the battle against the Islamic State will be long and hard and only the frontiers will change
