In recent years geographers and scholars from other disciplines have made substantial contributions to the literature on political violence, civil war and conflict within states through asking spatial questions: where is conflict likely to occur and how will it spread or diffuse? In this article, we provide a survey of the approaches, theories and methodologies used to address these questions and suggest avenues for advancing the spatial analysis of conflict. We argue that such conflicts are best conceived as an insurgency, defined as a violent political process to assert power and control over territorial space. After exploring the contributions of qualitative approaches (critical and feminist geopolitics) to our spatial understandings of these political processes, we examine quantitative research addressing these spatial questions. Specifically, we suggest that a network approach provides a useful perspective for understanding the power relations and spatial contestation of an insurgency. This approach also differentiates between escalation and diffusion, which are often treated synonymously in the literature.