In the days preceding the U.S.-led air strikes that pounded the Syrian city of Raqqa on Tuesday, many in the heart of the Islamic State in Iraq and the Levant (ISIL)’s self-declared caliphate welcomed the idea of strikes against their extremist rulers — even with little known about what seems likely to become a prolonged operation in their homeland.

The U.S. and partner nations – Jordan, Bahrain, Saudi Arabia, Qatar and the United Arab Emirates – conducted 15 strikes against ISIL targets in and around Raqqa and several other parts of Syria overnight Tuesday. More than 20 ISIL fighters were killed in Raqqa alone, according to the Syrian Observatory on Human Rights, a monitoring group.

The capital of ISIL’s self-declared caliphate, Raqqa has chafed under ISIL’s extremist brand of Islamic law ever since it exploited a power vacuum in rebel-held territory to begin governing parts of northern Syria last year. Activists in and from the city reached by Al Jazeera were enthusiastic about the prospect of military action against ISIL "safe havens," as promised by the Obama administration, which they considered the only recourse for their desperate situation.

“Yes, I want these strikes,” said one member of the anti-ISIL campaign Raqqa is Being Slaughtered Silently, whose name Al Jazeera has withheld for security reasons. “We’re the living dead here. Say a single word against our rulers and they can execute, crucify or stone us.”

But many questions remain about the administration's anti-ISIL strategy in Syria, the more politically complicated arena of the transnational ISIL insurgency. According to Joint Chiefs of Staff Chairman Gen. Martin Dempsey, who testified before the Senate Armed Services Committee last week, “This will not look like shock and awe because that is not how ISIL is organized, but it will be persistent and sustainable.”

Across the border in Iraq, where ISIL has seized large swathes of the north and west, U.S.-led air strikes are designed to support the efforts of anti-ISIL ground forces — principally, the Iraqi government and Kurdish security forces — to recapture territory from the extremists.

The ground component in Syria is ill-defined. Congress has approved an expanded arming and training program for those Syrian rebels dubbed "moderate" by the U.S. — the weakest faction on the battlefield in Syria — in the hope that they can serve as viable ground partners after aerial strikes, at the same time as fending off the army of Syrian President Bashar al-Assad.