Understanding the role of climate extremes and their impact on the carbon (C) cycle is increasingly a focus of Earth system science. Climate extremes such as droughts, heat waves, or heavy precipitation events can cause substantial changes in terrestrial C fluxes. On the other hand, extreme changes in C fluxes are often, but not always, driven by extreme climate conditions. Here we present an analysis of how extremes in temperature and precipitation, and extreme changes in terrestrial C fluxes are related to each other in 10 state-of-the-art terrestrial carbon models, all driven by the same climate forcing. We use model outputs from the North American Carbon Program Multi-scale Synthesis and Terrestrial Model Intercomparison Project (MsTMIP). A global-scale analysis shows that both droughts and heat waves translate into anomalous net releases of CO₂ from the land surface via different mechanisms: Droughts largely decrease gross primary production (GPP) and to a lower extent total respiration (TR), while heat waves slightly decrease GPP but increase TR. Cold and wet periods have a smaller opposite effect. Analyzing extremes in C fluxes reveals that extreme changes in GPP and TR are often caused by strong shifts in water availability, but for extremes in TR shifts in temperature are also important. Extremes in net CO₂ exchange are equally strongly driven by deviations in temperature and precipitation. Models mostly agree on the sign of the C flux response to climate extremes, but model spread is large. In tropical forests, C cycle extremes are driven by water availability, whereas in boreal forests temperature plays a more important role. Models are particularly uncertain about the C flux response to extreme heat in boreal forests.