Marine heatwaves (MHWs) are periods of extreme warm sea surface temperature that persist for days to months(1) and can extend up to thousands of kilometres(2). Some of the recently observed marine heatwaves revealed the high vulnerability of marine ecosystems(3-11) and fisheries(12-14) to such extreme climate events. Yet our knowledge about past occurrences(15) and the future progression of MHWs is very limited. Here we use satellite observations and a suite of Earth system model simulations to show that MHWs have already become longer-lasting and more frequent, extensive and intense in the past few decades, and that this trend will accelerate under further global warming. Between 1982 and 2016, we detect a doubling in the number of MHW days, and this number is projected to further increase on average by a factor of 16 for global warming of 1.5 degrees Celsius relative to preindustrial levels and by a factor of 23 for global warming of 2.0 degrees Celsius. However, current national policies for the reduction of global carbon emissions are predicted to result in global warming of about 3.5 degrees Celsius by the end of the twenty-first century(16), for which models project an average increase in the probability of MHWs by a factor of 41. At this level of warming, MHWs have an average spatial extent that is 21 times bigger than in preindustrial times, last on average 112 days and reach maximum sea surface temperature anomaly intensities of 2.5 degrees Celsius. The largest changes are projected to occur in the western tropical Pacific and Arctic oceans. Today, 87 per cent of MHWs are attributable to human-induced warming, with this ratio increasing to nearly 100 per cent under any global warming scenario exceeding 2 degrees Celsius. Our results suggest that MHWs will become very frequent and extreme under global warming, probably pushing marine organisms and ecosystems to the limits of their resilience and even beyond, which could cause irreversible changes.