Although its predecessor was active for several years following the US-led invasion of Iraq, IS sprang to worldwide prominence in June last year when it overran large parts of Iraq and Syria, declaring a "caliphate" in the two nations.
Several local jihadist groups quickly affiliated themselves, and IS has since received pledges of fealty from extremist outfits from as far afield as Algeria, Afghanistan and Indonesia.
- Widening affiliation -
But it is in Iraq and Syria -- where IS still controls huge portions of Sunni Arab heartland -- that the group holds the most sway.
According to Pieter van Ostaeyen, an expert on the Middle East, about eight million people live in territory controlled by IS in the two countries.
In Libya, where an IS affiliate recently killed 21 Coptic Christians in videotaped execution-style murders, "the territory isn't too large and isn't totally controlled by the jihadists," he said.
Luay al-Khatteeb, a researcher at the Brookings Institute, puts the number of people in IS-controlled areas at "between six and seven million".
From that, the jihadists have more than enough possible recruits to maintain "a powerful and numerous armed force," Khatteeb added.
- Unknown fighter numbers -
IS's strict controls on information from its territories make it virtually impossible to evaluate the number of fighters it has at its disposal, and estimates vary greatly.
Khatteeb said IS could have 80,000 fighters, including "around 20,000 foreigners".
Van Ostaeyen put the number at 60,000-70,000 -- the vast majority in Iraq and Syria -- and about 1,500-2,000 in Libya.
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The Syrian Observatory for Human Rights, a Britain-based monitor, estimates IS has as many as 45,000 fighters in Syria alone.
Dalia Ghanem-Yazbeck, an analyst from the Carnegie Middle East Center, believes the true size of IS' fighting force to be far smaller than most reports suggest.
"If they have 25,000 in total, that's the maximum," she said, adding that reporting inflated fighter figures amounted to "advertising" for IS.
- Funding -
It is no less challenging to work out how much money IS has, or where its funding comes from.
The group seized several oil fields when it swarmed across Iraq and Syria last year, and revenue from the crude trade is a key pillar of its income.
The US Treasury estimated in October that IS makes as much as $1 million per day from oil sales, even if some analysts dispute this figure.
Khatteeb said the group produces "a maximum of 50,000-60,000 barrels a day," not enough to satisfy demand for the population under its yoke.
He added that IS' income is supplemented by various activities, including the smuggling of antiques, taxes and extortion imposed on "merchants who have to pay to keep their shops open".
- 'Trademark that works' -
Although it has been pinned back militarily by US-led air strikes and a counter-offensive by Iraqi security forces and militias, IS remains a potent draw for would-be recruits.
Using social media and slick video productions, Ghanem-Yazbeck said the group had become its own trademark.
"It's a trademark that works, like Coca-Cola or McDonald's, which attracts," she said.
"Their true strengths are virtual, online, on YouTube... after nearly every defeat they put out a shocking video so that we talk about them. It's a way of compensating for military defeat."