In this study we investigate the scaling of precipitation extremes with temperature in the Mediterranean region by assessing against observations the present day and future regional climate simulations performed in the frame of the HyMeX and MED-CORDEX programs. Over the 1979-2008 period, despite differences in quantitative precipitation simulation across the various models, the change in precipitation extremes with respect to temperature is robust and consistent. The spatial variability of the temperature-precipitation extremes relationship displays a hook shape across the Mediterranean, with negative slope at high temperatures and a slope following Clausius-Clapeyron (CC)-scaling at low temperatures. The temperature at which the slope of the temperature-precipitation extreme relation sharply changes (or temperature break), ranges from about 20 A degrees C in the western Mediterranean to < 10 A degrees C in Greece. In addition, this slope is always negative in the arid regions of the Mediterranean. The scaling of the simulated precipitation extremes is insensitive to ocean-atmosphere coupling, while it depends very weakly on the resolution at high temperatures for short precipitation accumulation times. In future climate scenario simulations covering the 2070-2100 period, the temperature break shifts to higher temperatures by a value which is on average the mean regional temperature change due to global warming. The slope of the simulated future temperature-precipitation extremes relationship is close to CC-scaling at temperatures below the temperature break, while at high temperatures, the negative slope is close, but somewhat flatter or steeper, than in the current climate depending on the model. Overall, models predict more intense precipitation extremes in the future. Adjusting the temperature-precipitation extremes relationship in the present climate using the CC law and the temperature shift in the future allows the recovery of the temperature-precipitation extremes relationship in the future climate. This implies negligible regional changes of relative humidity in the future despite the large warming and drying over the Mediterranean. This suggests that the Mediterranean Sea is the primary source of moisture which counteracts the drying and warming impacts on relative humidity in parts of the Mediterranean region.