The Islamic State commands between 7,000 and 10,000 fighters, according to U.S. intelligence officials who spoke on condition of anonymity because they weren't authorized to brief the media.
Aymenn al-Tamimi, an expert on militant factions in Syria and Iraq, also put the group's fighting force at about 10,000, including veteran jihadi fighters from Iraq, the Gulf, North Africa and Europe. The Islamic State also relies on thousands of supporters to provide the public services expected of a "state," he said.
The foreigners' roles vary. Some, including Germans and Frenchmen, have carried out suicide bombings. Others, however, hold leadership positions. One of the most prominent commanders in Syria is an imposing ethnic Chechen with a flowing red beard who goes by the name of Omar al-Shishani.
The Islamic State has crafted its tactics and message to best meet local considerations.
"In Iraq, they portray themselves as the protectors of the Sunni community," al-Tamimi said. "In Syria, they are much more open about their ideology and project."
In the Syrian city of Raqqa, their strict brand of Islamic law holds sway. Activists and residents say music has been banned, Christians have to pay an Islamic tax for protection and people are executed in the main square.
In the Iraqi city of Fallujah, however, residents say the group has so far taken a more moderate approach, choosing to overlook some practices it considers forbidden.
The makeup of its forces also varies to a degree. In Syria, foreigners play a larger role than in Iraq, where locals tend to dominate.
The group has been able to do this, in part, because of the simmering anger in Iraq's Sunni minority community toward Shiite Prime Minister Nouri al-Maliki. They accuse al-Maliki of treating them as second-class citizens.