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Compound climate extremes, such as events with concurrent temperature and precipitation extremes, have significant impacts on the health of humans and ecosystems. This paper aims to analyze temporal and spatial characteristics of compound extremes of monthly temperature and precipitation, evaluate the performance of the sixth phase of the Coupled Model Intercomparison Project (CMIP6) models in simulating compound extremes, and investigate their future changes under Shared Socioeconomic Pathways (SSPs). The results show a significant increase in the frequency of compound warm extremes (warm/dry and warm/wet) but a decrease in compound cold extremes (cold/dry and cold/wet) during 1985–2014 relative to 1955–1984. The observed upward trends of compound warm extremes over China are much higher than those worldwide during the period of interest. A multi‐model ensemble (MME) of CMIP6 models performs well in simulating temporal changes of warm/wet extremes, and temporal correlation coefficients between MME and observations are above 0.86. Under future scenarios, CMIP6 simulations show substantial rises in compound warm extremes and declines in compound cold extremes. Globally, the average frequency of warm/wet extremes over a 30‐yr period is projected to increase for 2070–2099 relative to 1985–2014 by 18.53, 34.15, 48.79, and 59.60 under SSP1‐2.6, SSP2‐4.5, SSP3‐7.0, and SSP5‐8.5, respectively. Inter‐model uncertainties for the frequencies of compound warm extremes are considerably higher than those of compound cold extremes. The projected uncertainties in the global occurrences of warm/wet extremes are 3.82 times those of warm/dry extremes during 2070–2099 and especially high for the Amazon and the Tibetan Plateau. Plain Language Summary: Compound climate extremes, such as the events with concurrent temperature and precipitation extremes, have significant impacts on the health of humans and ecosystems. Can climate model simulate the historical compound extremes? If yes, how the global compound extremes will change in the future? In this study, we found that the global climate model performs well in simulating temporal changes of warm/wet and warm/dry extremes during the period 1955–2014. With greenhouse gas emissions continuing to increase in the future, compound warm/dry and warm/wet extremes show a continuous increase in frequency in the next few decades, while compound cold/dry and cold/wet extremes are projected to occur less frequently. Key Points: A multi‐model ensemble of CMIP6 models performs well in simulating temporal changes of warm/wet extremesThe inter‐model uncertainties for the frequencies of compound warm extremes are considerably higher than those of compound cold extremesThe projected uncertainties in the global occurrences of warm/wet extremes are 3.82 times those of warm/dry extremes during 2070–2099 [ABSTRACT FROM AUTHOR]