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Tropospheric anthropogenic aerosols contribute the second-largest forcing to climate change, but with high uncertainty owing to their spatio-temporal variability and complicated optical properties. In this Review, we synthesize understanding of aerosol observations and their radiative and climate effects. Aerosols offset about one-third of the warming effect by anthropogenic greenhouse gases. Yet, in regions and seasons where the absorbing aerosol fraction is high — such as South America and East and South Asia — substantial atmospheric warming can occur. The internal mixing and the vertical distribution of aerosols, which alters both the direct effect and aerosol–cloud interactions, might further enhance this warming. Despite extensive research in aerosol–cloud interactions, there is still at least a 50% spread in total aerosol forcing estimates. This ongoing uncertainty is linked, in part, to the poor measurement of anthropogenic and natural aerosol absorption, as well as the little-understood effects of aerosols on clouds. Next-generation, space-borne, multi-angle polarization and active remote sensing, combined with in situ observations, offer opportunities to better constrain aerosol scattering, absorption and size distribution, thus, improving models to refine estimates of aerosol forcing and climate effects.