Climate policy needs to respond to the realities of overshooting 1.5°C of warming. Geoengineering approaches – both large-scale carbon dioxide removal and solar radiation management – have been proposed as ways to both limit global temperature increase and return the climate to a stable and safe state. These provide policy makers with new options, but come with notable biophysical and socioeconomic risks. Current methodologies for assessing climate risk have potentially significant weaknesses when evaluating the risks generated by geoengineering. Given the potential for social and biophysical systems to produce complex and destabilising feedback loops, careful assessments of geoengineering must be conducted within holistic and integrative risk frameworks.