Stratocumulus clouds are the most area-dominant cloud type on Earth, covering one-fifth of the planet’s surface, and changes in their coverage may amplify rather than mitigate global warming, though this remains highly uncertain. A key challenge in climate science is therefore to predict how stratocumulus clouds will change in a warming world. The TurPhyCloud project brings together four teams from experimental and theoretical physics and meteorology to capture turbulent processes and cloud microphysics across many scales using high-resolution field campaigns and statistical models. Based on a new microphysics-informed Large-Eddy Simulation model (MiLES), which will be embedded into weather and climate models, TurPhyCloud aims to improve understanding of cloud–radiation–turbulence interactions and reduce uncertainties in climate and weather predictions.