Despite being almost completely unaccountable to any official ministry, the Shiite militias have been tasked by the government with a key role in the war against the Islamic State. Yet what we saw in Yengija laid bare the costs of relying on these groups. Beyond the main road, an entire neighborhood of two-story homes was razed and flattened, with concrete slab roofs heaped atop piles of rubble. Personal belongings, children’s toys, and furniture peeked out from under the debris, a poignant reminder of the Sunni Arab families who, until recently, had lived there. All these families had fled in August when the militia started battling the Islamic State fighters in the surrounding area.

The destruction was overwhelming. The only houses that remained standing shared one common feature — blackened exterior windows showing where the militia had set fire to them in their efforts to destroy whatever they could not loot.

Families that had been driven from their homes told us that when the militia arrived, they destroyed the families’ homes. Former residents told us that those who have tried to return are accused of being Islamic State members or sympathizers; some were held by the militia for days, blindfolded, questioned, and beaten — or simply disappeared. In the Peshmerga-controlled city of Kirkuk, we met Hamad, a government worker from Yengija. He told us that he had snuck back into the village undetected two weeks earlier to try to collect some of his family’s belongings after being told by neighbors that his home was undamaged. But when he arrived, he found his house emptied of its valuables and his neighborhood torched.