The budget for the operation also highlights the ambiguity surrounding when exactly America's campaign against ISIS began. During a press conference in late August, Rear Admiral John Kirby, the Pentagon press secretary, suggested that U.S. military engagement commenced on June 16, when Obama sent 275 troops to defend the U.S. Embassy in Baghdad. But according to Defense News, the Defense Department has since changed course, arguing that the operation in fact began on August 8, the day airstrikes started in Iraq. The Pentagon has not disclosed the price tag for U.S. military activity between June 16 and August 8, though Defense News estimates the cost during that period at around $400 million. All told, that would mean the U.S. has so far spent more than $1 billion on its campaign against ISIS.

Most importantly, the numbers serve as a guide not only to when this all began, but also to how it ends. In September, Obama pledged to "degrade and ultimately destroy" ISIS. Thus far, the president's campaign appears to be doing more degrading than destroying. Last week, The New York Times reported that the U.S.-led coalition and various forces on the ground have helped halt the Islamic State's rapid advance in Iraq and Syria, and even reversed some of the group's territorial gains in Iraq. Airstrikes have also forced the jihadists to ditch their military bases for civilian homes (and their flashy convoys for more discreet means of transportation), while depleting ISIS revenues by taking out oil wells and refineries controlled by the group. (Airstrikes aside, ISIS may also simply have alienated local populations and run out of marginalized, sympathetic, Sunni-majority areas to conquer.)

But nearly 800 airstrikes into the U.S.-led military operation, ISIS still controls sizable pockets of territory in Syria and Iraq (the shaded areas in the map below). Strikes have targeted the Islamic State's leaders and rank-and-file, but foreigners continue to join the group in large numbers, and its fighting force remains formidable.

U.S./Coalition Airstrikes Against ISIS in Iraq and Syria

Reuters

Top U.S. officials acknowledge that airstrikes can only do so much to counter the Islamic State. "The airstrikes are buying us time," General Ray Odierno, the Army chief of staff, told CNN in late October. It will take several years to "significantly degrade" ISIS, he said, and doing so will depend in great measure on the efforts of local ground forces such as the Iraqi army and Kurdish peshmerga. (The U.S. appears to be more concerned with dislodging ISIS in Iraq than in Syria, where it is focusing instead on neutralizing the group's command centers and revenue sources, and reportedly training Syrian opposition fighters to defend rather than seize territory.)

"Over time, if that's not working, then we're going to have to reassess and we'll have to decide whether we think it's worth putting other forces in there, to include U.S. forces," Odierno added.