This Special Issue (SI) of Space and Polity profiles the varied contributions of geographical inquiry to scholarly debates on the causes, meaning and implications of the UKs decision to Brexit from the EU. By way of framing the SI, this Introduction develops the argument that insofar as it is confronting, complicating and challenging geographical ideas and debates, Brexit recursively is intruding on and perhaps even implicating itself in the structuration of geographic thought and practice, most immediately in the UK and in European states particularly impacted (not least Ireland) and especially with respect to political geographical research. We develop this argument through five provocations, questioning the ways in which Brexit exists as a troubling reality for: a) critical policy studies; b) the project of decolonizing geography; c) historiographies of human territorialization and sovereignty; d) the status of evidence-based public policy in a post-political and post-truth age, and; e) the management of risk, hazards, and disasters. A completing/completed Brexit we conclude, may bequeath a tradition of ‘Brexit Geographies’ and therein leave an enduring signature on the history of Anglo-European geographic thought.