Solar geoengineering, also called sunlight reflection or solar radiation modification (SRM), is a potential climate response that would cool the Earth's surface and reduce many other climate changes by scattering on order 1% of incoming sunlight back to space. SRM can only imperfectly correct for elevated greenhouse gases, but it might complement other climate responses to reduce risks, while also bringing new risks and new challenges to global governance. As climate alarm and calls for effective near-term action mount, SRM is attracting sharply increased attention and controversy, with many calls for expanded research and governance consultations along with ongoing concerns about risks, misuse, or overreliance. We review SRM's history, methods, potential uses and impacts, and governance needs, prioritizing the approach that is most prominent and promising, stratospheric aerosol injection. We identify several policy-relevant characteristics of SRM interventions and identify four narratives that capture current arguments over how SRM might be developed or used in sociopolitical context to either beneficial or destructive effect, with implications for near-term research, assessment, and governance activity.