The Earth’s tropical oceans are covered by shallow cumulus clouds. Conventionally, these clouds have been treated as a homogeneous collection of small, puffy, precipitating plumes, around a kilometre in size. This thesis challenges that paradigm. We show that shallow cumulus clouds are patterned into mesoscale (10-500 km) structures in nature, uncover an intrinsic instability which explains why the convection can grow to such scales in models, assess the models’ ability to represent the cloud-circulation coupling underlying the instability, and confront the models with observations. We generalise our findings in realistic models of the subtropics, assembling key building blocks for a theory of shallow cloud-circulation coupling. Finally, we construct a large simulation ensemble of self-organising shallow cumulus clouds, and use this to show that self-organising processes are unlikely to change our best estimates of how shallow cumulus will feed back on a changing climate.