The Islamic State of Iraq and Syria, better known as ISIS, has claimed responsibility for the November 13 terrorist attacks in Paris. To really understand the group, the first thing you need to know about it is that it used to have a different name: al-Qaeda in Iraq.

US troops and allied Sunni militias defeated al-Qaeda in Iraq during the 2007 “surge” — but didn’t destroy it. The US commander in Iraq, General Ray Odierno, described the group in 2010 as down but “fundamentally the same.” In 2011, the group began rebuilding, and in 2012 and 2013 it freed a number of prisoners held by the Iraqi government, who then joined its ranks.

Meanwhile, the group saw an opportunity in Syria, where peaceful protests descended into violence in mid-2011 and 2012. It began establishing a presence in Syria in mid-2011 in order to participate in the fight against Bashar al-Assad’s regime, a move that helped it gain fighters and valuable battlefield experience.

In 2013, the group once known as al-Qaeda in Iraq — now based in both Syria and Iraq — rebranded as ISIS.

Tension grew between ISIS and al-Qaeda, and they formally divorced in February 2014. “Over the years, there have been many signs that the relationship between al Qaeda Central (AQC) and the group’s strongest, most unruly franchise was strained,” Barak Mendelsohn, a political scientist at Haverford College, writes. Their relationship “had always been more a matter of mutual interests than of shared ideology.”

According to Mendelsohn, disagreements over Syria pushed that relationship to the breaking point. ISIS claimed that it controlled Jabhat al-Nusra, the official al-Qaeda faction in Syria, and it defied orders from al-Qaeda’s leader, Ayman al-Zawahiri, to back off. “This was the first time a leader of an al-Qaeda franchise had publicly disobeyed,” he says. ISIS also defied repeated orders to kill fewer civilians in Syria, and the tensions led to al-Qaeda disavowing any connection with ISIS in a February communiqué.

Today, ISIS and al-Qaeda compete for influence over Islamist extremist groups around the world. Some experts believe ISIS may overtake al-Qaeda as the most influential group in this area globally.