Iraqi forces have entered a neighbourhood in West Mosul for the first time since launching an operation to retake it from so-called Islamic State (IS) five days ago.
It comes a day after troops retook the city's airport from IS.
The army's assault takes them from desert and farmland into a densely packed city, where fighting is expected to be particularly hard.
IS are dug into the west after being driven out of eastern Mosul last month.
Meanwhile, Iraq's prime minister announced that the country's air force had carried out its first strikes against IS in neighbouring Syria.
Haider al-Abadi said IS was attacked in two places from which it had carried out recent bombings in Baghdad.
The jihadist group is already being attacked in Syria by a multi-national air campaign as well as from anti-IS forces on the ground.
Earlier, Iraqi aircraft carried out heavy strikes on IS targets in western Mosul ahead of the ground attack on the city itself.
"This is where the real fighting starts," a colonel leading the operation told the BBC.
The BBC's Quentin Sommerville, who is embedded in the area with Iraqi police, said a small group of men had advanced inside the city from his position. They were driving an armoured bulldozer and other vehicles, while under fire.
He said this next stage of the battle would be even tougher, in narrow streets in a more heavily populated area.
It also includes districts seen as pro-IS.
Leaflets warning residents of an imminent offensive were earlier dropped over the west of the city.
The UN has voiced concern about the welfare of civilians trapped in western Mosul.
Aram Shakaram, the country deputy director for Save the Children in Iraq, told the BBC he believed relatively few people had been able to escape since Wednesday.
He said the charity believed that nearly 800,000 people were still trapped there.
'I could die in an air strike or be killed by IS' - Mohamed, activist
We are very scared, and we are worried that the final stages are going to take long.
IS will not give up and withdraw that easily and the whole operation might take as long as it did in east Mosul.
I won't lie, I am scared too and I don't know if I am going to die in an air strike or be killed by an IS fighter.
More than 160,000 people have fled their homes in and around the city.
The UN said in late January that almost half of all the casualties in Mosul were civilians.
All bridges linking the east and west of the city, across the Tigris river, have been destroyed by air strikes.
Taking the airport
The airport and the adjacent al-Ghazlani base are on Mosul's southern outskirts on the western side of the river.
When the airport was taken yesterday, the runway was found to have been destroyed by IS.
However, our correspondent says it still has value.
It is a large piece of land and controlling it will help secure southern routes to west Mosul, he says.
IS overran Mosul as they spread across much of northern and western Iraq in 2014.