Research into solar geoengineering, far from being societally neutral, is already highly intertwined with its emerging politics. This review outlines ways in which research conditions or constructs solar geoengineering in diverse ways, including the forms of possible material technologies of solar geoengineering; the criteria and targets for their assessment; the scenarios in which they might be deployed; the publics which may support or oppose them; their political implications for other climate responses, and the international relations, governance mechanisms and configurations of power that are presumed in order to regulate them. The review also examines proposals for governance of research, including suggested frameworks, principles, procedures and institutions. It critically assesses these proposals, revealing their limitations given the context of the conditioning effects of current research, and particularly highlights problems of the reproduction of Northern norms, instrumental approaches to public engagement, a weak embrace of precaution, and a persistent but questionable separation of research from deployment. It details complexities inherent in effective research governance which contribute to making the pursuit of solar geoengineering risky, controversial and ethically contentious. In conclusion it suggests a case for an explicit, reflexive research governance regime developed with international participation. It suggests that such a regime should encompass modelling and social science as well as field experimentation and must address not only technical and environmental but also the emergent social and political implications of research.