The Islamic State (IS), al-Qaeda-linked groups, Boko Haram and other extremist movements are protagonists in today’s deadliest crises, complicating efforts to end them. They have exploited wars, state collapse and geopolitical upheaval in the Middle East, gained new footholds in Africa and pose an evolving threat elsewhere. Reversing their gains requires avoiding the mistakes that enabled their rise. This means distinguishing between groups with different goals, using force more judiciously, ousting militants only with a viable plan for what comes next, and looking to open lines of communication, even with hardliners. Vital, too, is to de-escalate the crises they feed off and prevent others erupting, by nudging leaders toward dialogue, inclusion and reform and reacting sensibly to terrorist attacks. Most important is that action against “violent extremism” not distract from or deepen graver threats, notably escalating major- and regional-power rivalries.