Influences of aerosols on climate are qualitatively known, but the magnitude of their effects is uncertain with important implication for understanding past and future climate change. In this colloquium, I will explain some reasons for uncertainties in our understanding of aerosol effects on climate, and outline how we can make progress despite persistent multi-model spread in aerosol radiative forcing. We will see model-to-model differences for aerosol effects from global climate model simulations, and new CMIP aerosol data for use in climate simulations that inform the next IPCC assessment report of climate change. Looking ahead, I will introduce some of the plans for advancing the research field, e.g., through leading the new experiment protocol of the Aerosol and Chemistry Model Intercomparison Project, to which the most complex Earth system models currently available worldwide will contribute simulations.