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Heatwaves are consecutive hot days with devastating impacts on human health and the environment. These events may evolve across both space and time, characterizing a spatiotemporally contiguous propagation pattern that has not been fully understood. Here, we track the spatiotemporally contiguous heatwaves in both reanalysis datasets and model simulations and examine their moving patterns (i.e., moving distance, speed, and direction) in different continents and periods. Substantial changes in contiguous heatwaves have been identified from 1979 to 2020, with longer persistence, longer traveling distance, and slower propagation. These changes have been amplified since 1997, probably due to the weakening of eddy kinetic energy, zonal wind, and anthropogenic forcing. The results suggest that longer-lived, longer-traveling, and slower-moving contiguous heatwaves will cause more devastating impacts on human health and the environment in the future if greenhouse gas emissions keep rising and no effective measures are taken immediately. Our findings provide important implications for the adaption and mitigation of globally connected extreme heatwaves. [ABSTRACT FROM AUTHOR]