Three days after U.S. airstrikes in Iraq began, Islamic State militants fled west across the bridge spanning the Khazir River, destroying half of it with TNT.

The August explosion was meant to slow an offensive by Kurdish peshmerga forces to retake Iraqi towns seized by the Sunni Muslim extremist group. But the peshmerga created another path across the river and eventually regained control of a village in the shadow of the bridge.

In recent weeks, Kurdish fighters have made steady progress along this front line, pushing back Islamic State more than nine miles. But soon they are likely to find themselves on the far outskirts of Islamic State-controlled Mosul, Iraq’s second-largest city, where they will face what is more than just a military challenge. It will be one also fraught with political and sectarian considerations. […]