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Abstract Solar geoengineering refers to proposals, including stratospheric aerosol injection (SAI), to slow or reverse climate change by reflecting away incoming sunlight. The rapid changes ongoing in the Arctic and Antarctic, and the risk of exceeding tipping points in the cryosphere within decades, make limiting such changes a plausible objective of solar geoengineering. Here, we review the impacts of SAI on polar climate and cryosphere, including the dependence of these impacts on the latitude(s) of injection, and make recommendations for future research directions. SAI would cool the polar regions and reduce many changes in polar climate under future warming scenarios. Some under‐cooling of the polar regions relative to the global mean is expected under SAI without high latitude injection, due to latitudinal variation in insolation and CO2 forcing, the forcing dependence of the polar lapse rate feedback, and altered atmospheric dynamics. There are also potential limitations in the effectiveness of SAI to arrest changes in winter‐time polar climate and to prevent sea‐level rise from the Antarctic ice sheet. Finally, we also review the prospects for three other solar geoengineering proposals targeting the poles: marine cloud brightening, cirrus cloud thinning, and sea‐ice albedo modification. Sea‐ice albedo modification appears unlikely to be viable on pan‐Arctic or Antarctic scales. Whether marine cloud brightening or cirrus cloud thinning would be effective in the polar regions remains uncertain. Solar geoengineering is an increasingly prominent proposal and a robust understanding of its consequences in the polar regions is needed to inform climate policy in the coming decades.