Abstract: Solar geoengineering (also known as solar radiation modification) is garnering more attention (and controversy) among media and policymakers in response to the impacts of climate change. Such debates have become more prominent following the first-ever field trials of stratospheric aerosol injection (SAI) in 2022. The need for public engagement and governance is increasingly evident as discussions intensify about a prospective role for such technologies. Drawing on a global, large-scale set of nationally representative surveys (N = 30,284, in 30 countries and 19 languages) and focus groups (N=323 participants, in 44 groups in 22 countries), I provide a few targeted lessons to understand ongoing discussions about solar geoengineering. First, we find that global South groups exhibit greater hope but an arguably richer range of concerns for solar geoengineering, in the context of observable inequities in climate action and potential geopolitical conflict. Meanwhile, a strong, global preference for multilateral coordination and public engagement from the conduct of research onwards is offset by skepticism of effective multilateralism and public discourse. Second,  Global South publics are revealed to be significantly more favorable about potential benefits and express greater support for climate-intervention technologies. Conversely, Global South publics express greater concern that climate-intervention technologies could undermine climate-mitigation efforts, and that solar geoengineering could promote an unequal distribution of risks between poor and rich countries. Finally, public preferences are sketched for a variety of bottom-up and top-down engagement practices ranging from information recipient to broad decision authority. Here, we show that engagement practices need to be responsive to local political cultures and socio-technical environments, while attending to the global dimensions and interconnectedness of the issues at stake.