The group began in 2004 as al Qaeda in Iraq, before rebranding as ISIS two years later. It was an ally of -- and had similarities with -- Osama bin Laden's al Qaeda: both were radical anti-Western militant groups devoted to establishing an independent Islamic state in the region. But ISIS -- unlike al Qaeda, which disowned the group in early 2014 -- has proven to be more brutal and more effective at controlling territory it has seized.

ISIS is putting governing structures in place to rule the territories the group conquers once the dust settles on the battlefield. From the cabinet and the governors to the financial and legislative bodies, ISIS' bureaucratic hierarchy looks a lot like those of some of the Western countries whose values it rejects -- if you take away the democracy and add in a council to consider who should be beheaded.

Oil and land: What ISIS controls

The group seized control of Mosul, Iraq's second-largest city, this summer. But its power base is in Raqqa, eastern Syria, where ISIS is now in control of more than half of Syria's oil assets -- along with a number of oil fields in Iraq -- according to energy expert Luay al-Khateeb. Al-Khateeb says the oil is finding its way to the black market and could be making ISIS up to $3 million each day.

More than 11,000 people have traveled from abroad to fight in Syria and Iraq, officials suggest, although some have gone back home again. They align themselves with different factions, and sometimes change loyalties as groups merge, disband or change allegiances. Naturally, countries with bigger Muslim populations tend to send the largest number of fighters.

But some nations with relatively small Muslim populations have sent a disproportionately large number of jihadis. Finland, Ireland and Australia have the highest number of foreign fighters per capita, although Finnish security officials say a minority of Finns in their count went for humanitarian reasons.

CNN's Atika Shubert, Ivana Kottasova and Sean O'Key contributed to this report.