By interacting with radiation, clouds modulate the flow of energy through the Earth system, the circulation of the atmosphere, and regional climate. We review the impact of cloud‐radiation interactions for the atmospheric circulation in the present‐day climate, its internal variability and its response to climate change. After summarizing cloud‐controlling factors and cloud‐radiative effects, we clarify the scope and limits of the Clouds On‐Off Klimate Model Intercomparison Experiment (COOKIE) and cloud‐locking modeling methods. COOKIE showed that the presence of cloud‐radiative effects shapes the circulation in the present‐day climate in many important ways, including the width of the tropical rain belts and the position of the extratropical storm tracks. Cloud locking, in contrast, identified how clouds affect internal variability and the circulation response to global warming. This includes strong, but model‐dependent, shortwave and longwave cloud impacts on the El‐Nino Southern Oscillation, and the finding that most of the poleward circulation expansion in response to global warming can be attributed to radiative changes in clouds. We highlight the circulation impact of shortwave changes from low‐level clouds and longwave changes from rising high‐level clouds, and the contribution of these cloud changes to model differences in the circulation response to global warming. The review in particular draws attention to the role of cloud‐radiative heating within the atmosphere. We close by raising some open questions which, among others, concern the need for studying the cloud impact on regional scales and opportunities created by the next generation of global storm‐resolving models.