Much of it is uninhabited desert, but significant towns and cities in both countries, and almost a whole province in Syria, remain in the militants’ hands. Among them are staunch ISIS strongholds, located in some of the most remote terrain of the war. In some instances, it isn’t yet clear which forces will undertake the battles, and potential local and international flash points lie ahead as competing powers vie for the chance to control territory.

Raqqa: The five-week-old battle for the ISIS self-proclaimed capital of Raqqa is getting underway, launched by a U.S.-backed force of Kurds and Arabs known as the Syrian Democratic Forces and aided by U.S. Special Operations troops. In the first month, they took 20 percent of the city, according to Col. Ryan Dillon, a U.S. military spokesman. That doesn’t mean there another five months of combat left, however. Past battles have proved unpredictable, with the militants crumbling or fleeing in some places and putting up a stiff fight in others. Raqqa is smaller than Mosul and less densely populated, but there is no reason to believe they will defend it any less fiercely – and the battle for Mosul lasted nine months.

Bukamal (also known as Abu Kamal): This town on the Iraqi border is the southeasternmost of the Euphrates valley towns in Deir al-Zour province. The U.S. military has been trying to build a force of Syrian rebels capable of taking the town from a remote desert base 200 miles away. But their presence has created tensions between the United States and the Syrian operating nearby, who have now blocked the way. So it now seems most likely that the eventual battle for Bukamal will also fall to Syrian government loyalists, thereby putting them back in charge of the main highway linking Damascus to Baghdad.

Tal Afar: This mid-sized town around 30 miles west of Mosul is expected to be the next target of the military campaign in Iraq. It is renowned one of the ISIS most die-hard strongholds, with a long history of insurgency and is likely to put up stiff resistance. It is also one of the only towns in northwestern Iraq that has a sizable Shia population, which fled when the ISIS swept through in 2014. Now it is surrounded by Shia militias, and although there has not yet been a decision on whether they or the Iraqi army will undertake the offensive, Tal Afar could ignite future sectarian tensions.

Hawija: Located in an isolated pocket of mostly rural territory southwest of the Kurdish-controlled city of Kirkuk, Hawija is the easternmost of the ISIS territories. It is also known as an early outpost of ISIS sympathies. Hawija is likewise completely surrounded, on three sides by Kurdish peshmerga and to the south by the Iraqi army. There is no agreement yet on whether the Kurds or the Iraqi security forces, or both, will undertake the battle.