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There is an international effort to attempt to limit global warming to 1.5 degrees C above pre-industrial levels, however, there is a lack of quantitative analysis on the benefits of holding global warming to such a level. In this study, coupled climate model simulations are used to form large ensembles of simulated years at 1.5 degrees C and 2 degrees C of global warming. These ensembles are used to assess projected changes in the frequency and magnitude of European climate extremes at these warming levels. For example, we find that events similar to the European record hot summer of 2003, which caused tens of thousands of excess deaths, would be very likely at least 24% less frequent in a world at 1.5 degrees C global warming compared to 2 degrees C global warming. Under 2 degrees C of global warming, we could expect such extreme summer temperatures in the historical record to become commonplace, occurring in at least one-in-every-two years. We find that there are very clear benefits to limiting global warming for the European continent, including fewer and less intense heat and rainfall extremes when compared with higher levels of global warming.