Increases in concurrent climate extremes in different parts of the world threaten the ecosystem and our society. However, spatial patterns of these extremes and their past and future changes remain unclear. Here, we develop a statistical framework to test for spatial dependence and show widespread dependence of temperature and precipitation extremes in observations and model simulations, with more frequent than expected concurrence of extremes around the world. Historical anthropogenic forcing has strengthened the concurrence of temperature extremes over 56% of 946 global paired regions, particularly in the tropics, but has not yet significantly affected concurrent precipitation extremes during 1901-2020. The future high-emissions pathway of SSP585 will substantially amplify the concurrence strength, intensity, and spatial extent for both temperature and precipitation extremes, especially over tropical and boreal regions, while the mitigation pathway of SSP126 can ameliorate the increase in concurrent climate extremes for these high-risk regions. Our findings will inform adaptation strategies to alleviate the impact of future climate extremes.