Climate-related extreme events impose a heavy toll on humankind, and many will likely become more frequent in the future. The compound (joint) occurrence of different climate-related hazards and impacts can further exacerbate the detrimental consequences for society. By analyzing postprocessed data from the Inter-Sectoral Impact Model Intercomparison Project, we provide a global mapping of future changes in the compound occurrence of six categories of hazards or impacts related to climate extremes. These are: river floods, droughts, heatwaves, wildfires, tropical cyclone-induced winds and crop failures. In line with the existing literature, we find sharp increases in the occurrence of many individual hazards and impacts, notably heatwaves and wildfires. Under a medium-high emission scenario, many regions worldwide transition from chiefly experiencing a given category of hazard or impact in isolation to routinely experiencing compound hazard or impact occurrences. A similarly striking change is projected for the future recurrence of compound hazards or impacts, with many locations experiencing specific compound occurrences at least once a year for several years, or even decades, in a row. In the absence of effective global climate mitigation actions, we may thus witness a qualitative regime shift from a world dominated by individual climate-related hazards and impacts to one where compound occurrences become the norm.