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The compound of late winter snow droughts and early spring heatwaves (compound snow drought and heatwave (CSDHW)) could dramatically affect ecosystems and water availability, but has not been systematically investigated. Here we present a comprehensive assessment of CSDHW events and possible driving mechanisms. We find that 7% of the snow‐covered area experiences significant (p < 0.05) CSDHW events, and an average of 35% of snow droughts are followed by heatwaves during 1981–2020. The spatial extent of CSDHW is asymmetrically enlarging, with a significant increase in Eurasia and a relatively high fluctuation in North America. Specifically, the warm‐type CSDHW (i.e., snow drought with normal or above‐average precipitation followed by heatwave) occurs more frequently, with spatial coverage increasing faster than the dry‐type CSDHW (i.e., snow drought with below‐average precipitation followed by heatwave). In comparison, dry snow drought is more likely to be followed by heatwave due to intensified soil drought and atmospheric aridity. Plain Language Summary: Snow drought and heatwave events have adverse impacts on society and ecosystems, and have drawn much attention in the past decades. However, the consecutive occurrence of the two extreme events remains poorly understood. This study presents a global assessment of compound snow drought and heatwave (CSDHW) events for the period from 1981 to 2020. We find that more than one third (35%) of snow droughts are followed by heatwaves. The spatial extent of CSDHW is expanding globally, with a significant increase in Eurasia and a relatively high fluctuation in North America. Despite the higher frequency and expanding trend of the warm‐type CSDHW (i.e., snow drought with normal or above‐average precipitation followed by heatwave) than the dry‐type CSDHW (i.e., snow drought with below‐average precipitation followed by heatwave), dry snow drought is more likely to be followed by heatwaves, which can be attributed to intensifying soil drought and atmospheric aridity after dry snow drought. Key Points: There is a significant spatial expansion (13%) of compound snow drought and heatwave (CSDHW) events in the snow‐covered area of EurasiaThe warm‐type CSDHW becomes more frequent and expands faster than the dry‐type CSDHWDry snow drought promotes the occurrence of subsequent heatwave associated with intensified soil drought and atmospheric aridity [ABSTRACT FROM AUTHOR]