It will not be easy to defeat the brutal jihadists of Islamic State (IS), as the American-led coalition against the group aims to do.

IS is one of the best-financed terrorist organisations in the world, except for state-backed ones.

There is no credible estimate of the secretive group’s net worth, but in October 2014 an American official described it as amassing wealth at “a pretty massive clip”.

It pays fighters around $400 a month, which is more than Syrian rebel groups or the Iraqi government offer. It appears to have no trouble purchasing weaponry, either on the black market or from corrupt officials or militias. And it runs services (even if not always successfully) across the areas it controls, paying schoolteachers and providing for the poor and widowed. So where does it get all its cash from?

Without this wealth, IS, the latest evolution of al-Qaeda in Iraq, could not have expanded so rapidly. It only announced itself in its current form in March 2013 when it expanded into Syria from Iraq (subsequently parting ways with al-Qaeda).

It has since has fought to take over swathes of land in the two countries. By June 2013 it had taken control of Raqqa, a city in Syria, and in June 2014 it took over Mosul, Iraq’s second city. By then in control of an area that is home to 6m-8m people, it declared a caliphate at the end of that month.

Fighters have flocked to join the group. By September 2014 it was estimated to have 30,000 men (and some women, in a female police force), including 15,000 foreign fighters.

Unlike other terrorist groups, including al-Qaeda in Iraq, IS largely funds itself rather than relying on rich supporters (despite various versions of a conspiracy theory in the region that America, Iran or Israel bankrolls the group). Although IS receives donations, especially from Gulf-based financiers, they are a relatively insignificant contributor to its coffers.

Instead, the bulk of its money comes from oil revenues from fields under its control in western Iraq and eastern Syria. American officials estimated that it was making $2m a day from oil before air strikes started (locals reckon it was more) but in December an official said the strikes, some of which have been against oil facilities in Syria, meant the group's oil revenues had “significantly” dropped. Controlling so much land also helps IS make money from extortion and taxing people in the areas it controls.

Like other jihadist groups, it has learned that kidnapping can be profitable. IS earned at least $20m last year from ransoms paid for hostages, including several French and Spanish journalists.

The group cannot be defeated without cutting off its funds. That is why the coalition says it aims to attack the sources of its revenue as well as stopping the group from advancing militarily. America and its allies have carried out air strikes on IS-controlled oil refineries in Syria.

America and Britain, which have a strict policy against paying ransoms for hostages, are pressuring European countries to stop paying up (something they deny doing).

Several countries have applied sanctions against IS leaders as well as those known to raise funds for the group. But officials are keen to emphasise it will be a long fight. For now, IS still seems to be able to pay for everything it needs.