Maps often depict the Islamic State as a sprawling territory across Iraq and Syria. But the group’s control has been shaped by about 126 places — cities, towns, infrastructure and bases — where it has had military dominance.

Out of 10 Cities, the Islamic State Remains in Six The group has been forced out of about 55 places where it once had control, including four major cities, since it made rapid advances across the two countries in 2014. And it could soon lose Falluja, the first city it controlled.

The Militants Capture Infrastructure and Resources to Generate Revenue As they seized cities, Islamic State militants also captured valuable resources like oil fields and hydroelectric dams, which have helped them generate income. The group’s oil and gas revenue is down 26 percent since last year but still adds up to about $23 million a month, according to IHS.

The Group Has Maintained a Nearly Continuous Hold Along the Euphrates River The Islamic State has contested or controlled many towns along the Euphrates River since as early as January 2014, giving them access to important roads and infrastructure that connect their territory across Syria and Iraq. The town of Mayadin, which in 2004 had a population of about 44,000, is important to the Islamic State as an uncontested administrative center that is close to one of its major oil fields.

The Islamic State Is Fighting to Keep a Key Corridor to Turkey. After losing a months long battle with Kurdish forces for control of Kobani, a key Syrian town on the border with Turkey, the Islamic State was quickly pushed out of a large stretch of northern Syria. Now, the Islamic State is fighting to hold onto a strategic corridor at the Turkish border that allows their people and goods to move between the two countries.

The Militants Often Capture Weapons Along With Military Bases Many of the weapons used by Islamic State fighters have come from military facilities that the group has seized from the Iraqi and Syrian governments. In January, the Islamic State had its largest weapons windfall when it took control of the Ayyash Arms Depot in Syria, capturing an estimated two million rounds of ammunition, 9,000 grenades and 100 antitank missiles.

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