Heatwaves are becoming increasingly frequent and extreme under a changing climate, with devastating effects on a wide range of sectors, including human health and ecosystems. The basic ingredients for heatwaves – and in particular, their interaction – are however not yet fully understood. These ingredients include the dynamics of the atmosphere, the land and ocean surface, atmospheric moisture, and land topography. Several of these ingredients experience drastic changes in a changing climate, and it is therefore crucial to understand their relative and combined contributions to heat extremes in present and future climates. This project aims at resolving this issue by building a process-based hierarchy of numerical models ranging from a dry dynamical core model to a prediction system using full physics. With this approach, the necessary ingredients for heatwaves can be evaluated and their relative and combined contribution to heatwaves can be understood. While solving a fundamental question in atmospheric fluid dynamics, the proposed research also aims to improve the predictability of heat extremes, thereby extending the warning horizon and minimizing the societal consequences for future heat waves.