Internationalisation of higher education has diverging implications for climate change, on the one hand entailing greenhouse gas emissions through mobility, but also contributing to climate action through international collaboration. These apparent contradictions and resulting trade-offs present significant challenges to universities. This paper puts forward a framework for understanding the combination of impacts, the interactions between them and implications for the climate crisis. It distinguishes between three dimensions of internationalisation: actors (movements of students and staff), practices (integration of the international into curriculum and research) and influence (the global reach of the various impacts of the university). Internationalisation in these three dimensions can have positive or negative implications for climate action and sustainability, through direct impacts (greenhouse gas emissions) and indirect ones (changes in individuals, societal structures, knowledge and technologies). Implications are drawn out for the actions and strategies of universities, as well as for the global system of higher education.