Governments-in-exile are conventionally viewed as discrepant forms of political practice and geopolitical exceptions to the rules of sovereign statehood. However, despite significant limitations, polities such as the Tibetan Government-in-Exile enact state-like functions and are actively forging new political spaces and modalities of sovereignty. Contextualising governments-in-exile with regards to a range of twentieth-century geopolitical anomalies, this study argues that such polities raise key questions for political geographers regarding the relationship between sovereignty and territory, the nature of statehood and the role of ‘the exception’ in geopolitical discourses. In light of contemporary critical reappraisals of sovereignty, territory and statehood, this study calls for political geography – and critical geopolitics in particular – to expand its gaze and engage with issues raised by governments-in-exile. In turn, an empirical and theoretical focus on such non-state entities highlights the utility of ethnographic methodologies within critical geopolitics, enables a critical fusion of literatures of the state and of statelessness, problematises taken-for-granted political geography categories and facilitates critical inquiry into alternative political arrangements.