Although uniquely destructive and wasteful, intergroup conflict and warfare are not confined to humans. They are seen across a range of group-living species, from social insects, fishes and birds to mammals, including nonhuman primates. With its unique collection of theory, research and review contributions from biology, anthropology and economics, this theme issue provides novel insights into intergroup conflict across taxa. Here, we introduce and organize this theme issue on the origins and consequences of intergroup conflict. We provide a coherent framework by modelling intergroup conflicts as multi-level games of strategy in which individuals within groups cooperate to compete with (individuals in) other groups for scarce resources, such as territory, food, mating opportunities, power and influence. Within this framework, we identify cross-species mechanisms and consequences of (participating in) intergroup conflict. We conclude by highlighting crosscutting innovations in the study of intergroup conflict set forth by individual contributions. These include, among others, insights on how within-group heterogeneities and leadership relate to group conflict, how intergroup conflict shapes social organization and how climate change and environmental degradation transition intergroup relations from peaceful coexistence to violent conflict.