By many measures, Islamic State is a weakened and demoralized force. After months of U.S.-led bombing and defeats by local troops in Iraq and Syria, the group lost thousands of its fighters, was forced to relinquish significant territory and has been cut off from routes it used to move weapons and reinforcements.

But the group remains a potent threat in other ways, especially in its ability to inspire self-radicalized militants to carry out attacks in the West and elsewhere.

The man accused of carrying out a bombing in New York on Sept. 17 appears to have been inspired — if not directed — by the leaders and ideologues of al-Qaida and IS. The 28-year-old suspect, Ahmad Rahami, wrote admiringly in a journal about al-Qaida leader Osama bin Laden, American-born radical Islamic preacher Anwar al-Awlaki — who was killed in Yemen by a U.S. drone strike — and leading Islamic State strategist Abu Mohammad al-Adnani.