Black carbon (BC) aerosols are short-lived climate pollutants with important, but uncertain, climate impacts. In this Review, we synthesize observations of atmospheric BC concentrations, sources, optical properties, lifetimes and climate effects, drawing comparisons with atmospheric model simulations. Isotopic fingerprinting reveals regional differences in BC sources, with biomass burning contributing 93 ± 3% in sub-Saharan Africa, 56 ± 7% in South Asia and 28 ± 5% in East Asia. Atmospheric BC loadings have declined in South America, East Asia, Europe and North America, and stabilized in Africa and South Asia owing to clean air policies and advances in technology and practices. The optical properties of BC influence its climate effects. The global-mean mass absorption coefficient (MAC550) of atmospheric BC is 12.3 ± 5.8 m2 g−1, being highest in Africa, Europe and South Asia. MAC550 is enhanced near universally by 1.6 ± 0.4 owing to ageing during long-range transport. In major emission regions, the aerosol absorption optical depth and the direct aerosol radiative forcing ratio between the bottom and the top of the atmosphere are lower in model simulations than in observations by factors of 2 and 1.5, respectively. Relative to long-term observations, model simulations estimate higher BC deposition fluxes but lower concentrations and sunlight absorption. These discrepancies have implications for the accuracy of model representations of humidity, clouds, precipitation and climate forcing. Future research should prioritize comparisons of emission inventory and model estimates with observations to enhance model accuracy and guide mitigation efforts.