As the prospect of average global warming exceeding 1.5°C becomes increasingly likely, interest in supplementing mitigation and adaptation with solar geoengineering (SG) responses will almost certainly rise. For example stratospheric aerosol injection to cool the planet could offset some of the warming for a given accumulation of atmospheric greenhouse gases. However, the physical and social science literature on SG remains modest compared with mitigation and adaptation. We outline three research themes for advancing policy-relevant social science related to SG: (i) SG costs, benefits, risks, and uncertainty; (ii) the political economy of SG deployment; and (iii) SG’s role in a climate strategy portfolio.