Who are the jihadi extremists storming through Iraq — and what do they want?

If you map out all of the towns and cities that the militants of the Islamic State of Iraq and the Levant, known as ISIL or ISIS, have seized control over, a wide half-moon shape emerges that stretches from Aleppo, Syria in the northwest to the outskirts of the Iraqi capital of Baghdad to the southeast.

It is more evidence of the stunning success of a group US officials call “one of the most dangerous terrorist groups in the world.”

The Long War Journal mapped it all out here. Bill Roggio is the editor there and the following is an edited transcript of an interview with him and The World's Matthew Bell.

Q: Tell us a little about the arc of influence that shows up in your map of areas controlled by ISIS.  

We knew that ISIS was in control of much of the Euphrates River valley in Iraq since the beginning of the year. In Syria, [ISIS] has actually lost some ground near Aleppo due to its infighting with other rebel groups. But the gains that it has made in Iraq over the last several days really are astounding. The group is now essentially in control of about a quarter to a third of Iraq. Just today, it advanced into the city of Baiji, which hosts the largest oil refinery in Iraq. It's advancing on Tikrit and controls much of that city, which is the capital of Salahuddin Province. Looking at this map, it's not good news. If the Iraqi government can't retake control of Fallujah, which has been under ISIS's control since the beginning of the year — and that's just outside of Baghdad — how do they expect to advance hundreds of miles north to retake Mosul. Unless they can get the Kurdish forces back on their side, and the Kurds want to go up against ISIS in Mosul and other areas.

Q: How much of a threat does ISIS pose to Baghdad at this point?

It's significant. Keep in mind, we captured a map from the predecessor of ISIS, which was al-Qaeda in Iraq, back in 2007. And they had a whole plan to take over Baghdad and what they called "the belts." And basically, the plan is to take key areas around Baghdad and then you take control of the provinces. I think that's exactly what [ISIS] is doing, putting this plan into effect. I think we're going to — at some point — see some kind of seige of Baghdad.

Q: Remind us what this group is. Who is ISIS and what do they want?

ISIS used to be al-Qaeda in Iraq. There's a division between the groups now, due to a leadership dispute over how the jihad was to be conducted inside Syria. So, al-Qaeda essentially disowned them. But they are a jihadist group just like Al Qaeda. They seek to impose an Islamic caliphate and their harsh version of sharia law, or Islamic law. And they want to do it throughout the region. ISIS has threatened the United States. They were our sworn enemy inside Iraq and this is essentially the same group that the US fought in Iraq up until 2011. Now, they're just bigger and stronger. Just like al-Qaeda, ISIS is recruiting suicide bombers from all over the world. But ISIS is basically the reincarnation of al-Qaeda in Iraq.

Q: Should we stop referring to ISIS as a 'stateless entity'? After all, they're in control of a lot of territory now.

It's early, but what we know is that ISIS has held territory from Aleppo in Syria to central Iraq. They've held parts of Iraq for the last six months and in Syria for much longer. The question is, how long can ISIS maintain these recent gains in Mosul and central and northern Iraq? But the Syrian security forces have not been able to eject these guys for some time, and the same goes for the Iraqis in Anbar. So, at some point, they are the state. They have the nucleus of their caliphate and they're not going to stop.

Q: But if you put your military analyst's hat on, could ISIS be overextending itself at this point?

It certainly is possible. But keep in mind what it took for the US to drive al-Qaeda in Iraq back underground. We had a surge of more than 130,000 US troops and a military operation from the best military in the world with intelligence, airpower, and an operation that spanned well over a year. I think ISIS might be calculating right now that the Iraqis probably don't have that in them. And since the US isn't there to help, I think their calculation is, "let's see if they can take it back from us." [Iraqi government forces] have been unsuccessful in taking back Fallujah and the Euphrates River valley. The Syrians are incapable of doing it inside Syria. If they start approaching Baghdad, they might be overreaching. Also, the other element again is, what are the Kurds going to do? Are the Kurds going to sort of draw their battle lines and keep ISIS out of those areas of control? Or, are they going to throw in their lot with the Iraqi government and try to retake Mosul and other areas around Tikrit and Kirkuk? The Kurds are a very well-organized [military] force. Are they going to fight ISIS, or just withdraw and protect their territory?

Q: What about the signs so far from the Iraqi security forces? How are they doing?

They've been awful. And that's why they've lost all this territory. In Mosul, for reasons yet unknown, they abandoned military equipment, ditched their clothing, they left arms and ammunition and fled. This is apparently happening all the way down to Tikrit. The military is just crumbling. They've performed poorly in Fallujah and elswhere in Anbar Province. Again, I think this is critical in ISIS's calculations. They are seeing a weak military that is incapable of sustaining itself in the field. This may all change if they advance into areas north of Baghdad, or the Baquba area, where it's mixed Sunni and Shia. [ISIS] may overreach if they keep advancing to the south of Baghdad. But still, Iraqi security forces are going to have a hard time clearing and holding these areas that ISIS has taken without the help of the Kurds and other powers.