The Aerosol Chemistry Model Intercomparison Project (AerChemMIP) was endorsed by the Coupled Model Intercomparison Project 6 (CMIP6) and was designed to quantify the climate and air quality impacts of aerosols and chemically reactive gases. AerChemMIP provided the first consistent calculation of effective radiative forcing (ERF) for a wide range of forcing agents, which was a vital contribution to the Sixth Assessment Report (AR6) of the Intergovernmental Panel on Climate Change. It supported the quantification of composition–climate feedback parameters and the climate response to short-lived climate forcers (SLCFs), as well as enabled the future impacts of air pollution mitigation to be identified, and the study of interactions between climate and air quality in a transient simulations. Here we review AerChemMIP in detail and assess the project against its stated objectives, its contribution to the CMIP6 project, and the wider scientific efforts designed to understand the role of aerosols and chemistry in the Earth system. We assess the successes of the project and the remaining challenges and gaps. We conclude with some recommendations that we hope will provide input to planning for future MIPs in this area. In particular, we highlight the necessity of sufficient ensemble size for the attribution of regional climate responses and the need for coordination across projects to ensure key science questions are addressed. Summary data for CMIP6 and AerChemMIP models such as model components, model configurations, and emergent quantities are included.