Civil wars that appear to observers to be the most complex—even using a colloquial understanding of the concept—are also those that seem to register the most intense fighting, the most prolonged spells of war, and the most resistance to durable conflict resolution. But what does it really mean for a civil war to be complex? We currently lack a concept of “civil war complexity” that can help us better understand the most important variations in civil wars across time and space. To address this gap we develop a conceptualization of “civil war complexity” consisting of three dimensions—“actor complexity,” “behavior complexity,” and “issue complexity”—and demonstrate how they manifest empirically. We also highlight this conceptualization’s utility—and the danger of overlooking it—through the case of Darfur. This conceptualization paves the way for a new research agenda that explores how civil wars differ in terms of their complexity, the causes and consequences of civil war complexity, and how to refine conflict resolution techniques and strategies.