Global warming is anticipated to intensify the hydrological cycle. However, this is neither expected to be globally uniform nor is the relationship between temperature increase and rainfall intensities expected to be linear. The objective of this study is to assess changes in annual rainfall extremes, total annual precipitation, and their relationship in the larger Mediterranean region. We use an up-to-date ensemble of 33 regional climate simulations from the EURO-CORDEX initiative at 0.11° resolution. We analyse the significance of trends for 1951-2000 and 2001-2100 under a 'business-as-usual' pathway (RCP8.5). Our future projections indicate a strong north/south Mediterranean gradient, with significant, decreasing trends in the magnitude of daily precipitation extremes in the south and the Maghreb region (up to -10 mm/decade) and less profound, increasing trends in the north. Despite the contrasting future trends, the 50-year daily precipitation extremes are projected to strongly increase (up to 100%) throughout the region. The 100-year extremes, derived with traditional extreme value approaches from the 1951-2000 simulations, underestimate the magnitude of these extreme events in the 2001-2100 projections by 30% for the drier areas of the Mediterranean (200-500 mm average annual rainfall) and by up to 20-30% for the wetter parts of the region. These 100-year extremes can occur at any time in any Mediterranean location. The contribution of the wettest day per year to the annual total precipitation is expected to increase (5-30%) throughout the region. The projected increase in extremes and the strong reductions in mean annual precipitation in the drier, southern and eastern Mediterranean will amplify the challenges for water resource management.