Climate engineering (geoengineering) is rising up the global policy agenda, partly because international divisions pose deep challenges to collective climate mitigation. However, geoengineering is similarly subject to clashing interests, knowledge-tradi- tions and geopolitics. Modelling and technical assessments of geoengineering are facilitated by assumptions of a single global planner (or some as yet unspecified rational governance), but the practicality of international governance remains mostly spec- ulative. Using evidence gathered from state delegates, climate activists and modellers, we reveal three underlying and clash- ing ‘geofutures’: an idealised understanding of governable geoengineering that abstracts from technical and political realities; a situated understanding of geoengineering emphasising power hierarchies in world order; and a pragmatist precautionary understanding emerging in spaces of negotiation such as UN Environment Assembly (UNEA). Set in the wider historical con- text of climate politics, the failure to agree even to a study of geoengineering at UNEA indicates underlying obstacles to glo- bal rules and institutions for geoengineering posed by divergent interests and underlying epistemic and political differences. Technology assessments should recognise that geoengineering will not be exempt from international fractures; that deploy- ment of geoengineering through imposition is a serious risk; and that contestations over geofutures pertain, not only to cli- mate policy, but also the future of planetary order.