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 analysing postprocessed data from the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP), 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. The use of impact model data provides a unique perspective on the compound occurrence of these hazards and impacts, beyond what can be obtained from Global Climate Model output. 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. Moreover, we show a nonlinearity in compound occurrences for different global warming levels, with higher warming giving a faster-than-linear increase in compound occurrences. 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.