Solar geoengineering has been proposed as a means to cool the Earth by increasing the reflection of sunlight back to space, for example, by injecting reflective aerosol particles (or their precursors) into the lower stratosphere. Such proposed techniques would not be able to substitute for mitigation of greenhouse gas (GHG) emissions as a response to the risks of climate change, as they would only mask some of the effects of global warming. They might, however, eventually be applied as a complementary approach to reduce climate risks. Thus, the Earth system consequences of solar geoengineering are central to understanding its potentials and risks. Here we review the state-of-the-art knowledge about stratospheric sulfate aerosol injection and an idealized proxy for this, ‘sunshade geoengineering,’ in which the intensity of incoming sunlight is directly reduced in models. Studies are consistent in suggesting that sunshade geoengineering and stratospheric aerosol injection would generally offset the climate effects of elevated GHG concentrations. However, it is clear that a solar geoengineered climate would be novel in some respects, one example being a notably reduced hydrological cycle intensity. Moreover, we provide an overview of nonclimatic aspects of the response to stratospheric aerosol injection, for example, its effect on ozone, and the uncertainties around its consequences. We also consider the issues raised by the partial control over the climate that solar geoengineering would allow. Finally, this overview highlights some key research gaps in need of being resolved to provide sound basis for guidance of future decisions around solar geoengineering.