The mechanisms leading to the occurrence of extreme weather and climate events are varied and complex. They generally encompass a combination of dynamic and thermodynamic processes, as well as drivers external to the climate system, such as anthropogenic greenhouse gas emissions and land use change. Here we present the ExtremeX multi-model intercomparison experiment, which was designed to investigate the contribution of dynamic and thermodynamic processes to recent weather and climate extremes. The numerical experiments are performed with three Earth system models: CESM, MIROC, and EC-Earth. They include control experiments with interactive atmosphere and land surface conditions, as well as experiments wherein the atmospheric circulation, soil moisture, or both are constrained using observation-based data. The temporal evolution and magnitude of temperature anomalies during heatwaves are well represented in the experiments with a constrained atmosphere. However, the magnitude of mean climatological biases in temperature and precipitation are not greatly reduced in any of the constrained experiments due to persistent or newly introduced biases. This highlights the importance of error compensations and tuning in the standard model versions. To show one possible application, ExtremeX is used to identify the main drivers of heatwaves and warm spells. The results reveal that both atmospheric circulation patterns and soil moisture conditions substantially contribute to the occurrence of these events. Soil moisture effects are particularly important in the tropics, the monsoon areas, and the Great Plains of the United States, whereas atmospheric circulation effects are major drivers in other midlatitude and high-latitude regions.