AbstractEarth system models (ESMs) are our main tools for quantifying the physical state of the Earth and predicting how it might change in the future under ongoing anthropogenic forcing. In recent years, however, artificial intelligence (AI) methods have been increasingly used to augment or even replace classical ESM tasks, raising hopes that AI could solve some of the grand challenges of climate science. In this Perspective we survey the recent achievements and limitations of both process-based models and AI in Earth system and climate research, and propose a methodological transformation in which deep neural networks and ESMs are dismantled as individual approaches and reassembled as learning, self-validating and interpretable ESM–network hybrids. Following this path, we coin the term neural Earth system modelling. We examine the concurrent potential and pitfalls of neural Earth system modelling and discuss the open question of whether AI can bolster ESMs or even ultimately render them obsolete.