Solar radiation modification (SRM) is increasingly discussed as a potential method to ameliorate some negative effects of climate change. However, unquantified uncertainties in physical and environmental impacts of SRM impede informed debate and decision making. Some uncertainties are due to lack of understanding of processes determining atmospheric effects of SRM and/or a lag in development of their representation in models, meaning even high-quality model intercomparisons will not necessarily reveal or address them. Although climate models at multiple scales are advancing in complexity, there are specific areas of uncertainty where additional model development (often requiring new observations) could significantly advance understanding of SRM's effects, and improve our ability to assess and weigh potential risks against those of choosing to not use SRM. We convene expert panels in the areas of atmospheric science most critical to understanding the three most widely discussed forms of SRM. Each identifies three key modeling gaps relevant to either stratospheric aerosols, cirrus, or low-altitude marine clouds. Within each area, key challenges remain in capturing impacts due to complex interactions in aerosol physics, atmospheric chemistry/dynamics, and aerosol-cloud interactions. Across all three, in addition to arguing for more observations, the panels argue that model development work to either leverage different capabilities of existing models, bridge scales across which relevant processes operate, or address known modeling gaps could advance understanding. By focusing on these knowledge gaps we believe the modeling community could advance understanding of SRM's physical risks and potential benefits, allowing better-informed decision-making about whether and how to use SRM.