October 21, 2016 6:18 AM EDT

IRAQ’S ARMY

The country’s military is fighting to undo the disastrous legacy of losing the Sunni-majority city to ISIS in June 2014. The troops are pushing toward Mosul from the south and will lead the assault on the city center.

PESHMERGA

Kurdish militias known collectively as the peshmerga, or “those who face death,” took a series of villages from ISIS on Oct. 17. Mosul is adjacent to the area controlled by the Kurdish regional government.

SHI’ITE FIGHTERS

Powerful militias dominated by Shi’ites, known as the Popular Mobilization Units, are fighting but not expected to enter the city center because of past allegations of abuses against Sunni Iraqis.

U.S.-LED FORCES

The international military coalition provides air support, artillery fire and special-operations forces on the ground. There are now more than 5,000 U.S. troops on the ground in Iraq, the most since 2009.

This appears in the October 31, 2016 issue of TIME.

Contact us at editors@time.com.

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