The Islamic State grew out of the “al-Qaeda in Iraq” franchise group in the late 2000s, which nominally was directed by the remnants of the al-Qaeda leadership. By the time the Syrian civil war was in full flow the group had split from al-Qaeda and renamed itself. At first it was known by the outside world as ISIL (Islamic State of Iraq and the Levant) but as the Arabic word for the Levant is al-Sham, gradually it became ISIS.
