The fight for Fallujah: On the front lines against ISIS

Progress slow, but steady in effort to reclaim Fallujah from ISIS

Iraqi forces, with support from U.S.-led airstrikes, are advancing on the city of Fallujah, fighting to free it from the grip of ISIS forces.

ISIS has held the city, a provincial capital about 40 miles west of Baghdad, for more than two years.

CBS News was with Iraqi special forces on the front lines Sunday along the southern outskirts of Fallujah.

These elite troops, trained by the U.S., are described by U.S. officials as the most competent fighting force in the country.

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Progress is slow but steady, with the troops advancing perhaps 500 yards a day. As they get closer to Fallujah, they're facing stiff resistance from ISIS fighters in the form of snipers, mortar fire, and an extensive network of roadside bombs. Car bombs are also a constant threat.

Iraqi commanders credit airstrikes by the U.S. and its allies with being a game-changer on the battlefield -- responsible for 75 percent of the success they've had so far in beating back ISIS in Iraq.

While CBS News was there, jets could be heard roaring overhead, followed two or three huge explosions. Officials said they struck their targets, a number of ISIS fighters holed up in a building.

But as Iraqi forces close in on the city, it will become more difficult to depend on air support. Tens of thousands of civilians -- including an estimated 20,000 children -- remain trapped inside Fallujah, where airstrikes could kill innocent people.

Commanders say they don't know how soon they'll be ready to enter the city itself, but that's when the real battle will begin: street-by-street urban combat against an enemy that's had two years to dig in.

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