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Abstract Carbon fluxes at the land‐atmosphere interface are strongly influenced by weather and climate conditions. Yet what is usually known as “climate extremes” does not always translate into very high or low carbon fluxes or so‐called “carbon extremes.” To reveal the patterns of how climate extremes influence terrestrial carbon fluxes, we analyzed the interannual variations in ecosystem carbon fluxes simulated by the Terrestrial Biosphere Models (TBMs) in the Inter‐Sectoral Impact Model Intercomparison Project. At the global level, TBMs simulated reduced ecosystem net primary productivity (NPP; 18.5 ± 9.3 g C m⁻² yr⁻¹), but enhanced heterotrophic respiration (Rh; 7 ± 4.6 g C m⁻² yr⁻¹) during extremely hot events. TBMs also simulated reduced NPP (60.9 ± 24.4 g C m⁻² yr⁻¹) and reduced Rh (16.5 ± 11.4 g C m⁻² yr⁻¹) during extreme dry events. Influences of precipitation extremes on terrestrial carbon uptake were larger in the arid/semiarid zones than other regions. During hot extremes, ecosystems in the low latitudes experienced a larger reduction in carbon uptake. However, a large fraction of carbon extremes did not occur in concert with either temperature or precipitation extremes. Rather these carbon extremes are likely to be caused by the interactive effects of the concurrent temperature and precipitation anomalies. The interactive effects showed considerable spatial variations with the largest effects on NPP in South America and Africa. Additionally, TBMs simulated a stronger sensitivity of ecosystem productivity to precipitation than satellite estimates. This study provides new insights into the complex ecosystem responses to climate extremes, especially the emergent properties of carbon dynamics resulting from compound climate extremes.