Realistic simulation of the Earth’s mean-state climate remains a major challenge, and yet it is crucial for predicting the climate system in transition. Deficiencies in models’ process representations, propagation of errors from one process to another, and associated compensating errors can often confound the interpretation and improvement of model simulations. Here we show that a significantly improved global atmospheric simulation can be achieved by focusing on the realism of process assumptions in cloud and subgrid processes. Process-oriented diagnostics provide insights into model deficiencies for targeted improvements. The development of new cloud and subgrid processes are informed by our understanding of physical mechanisms, which leads to significant improvements in clouds and precipitation climatology, reducing common and long-standing biases across cloud regimes. The sensitivity of clouds to aerosol and surface temperature perturbations is significantly reduced. We conclude that process-, mechanistic, and system- level understanding is necessary for achieving realistic predictions of climate evolution for the right reason.