Since early March 2014, the NASA/JAXA Global Precipitation Measurement Core- Observatory (GPM-CO) satellite has allowed analysis of precipitation systems around the globe, thanks to the capabilities of the GPM Microwave Imager (GMI) and Dual-Frequency Precipitation Radar (DPR). In this work, we demonstrate how GPM-CO measurements obtained from 4 years of observations over the Mediterranean area can be used as an extremely effective tool to study the main climatological characteristics of the most intense Mediterranean storm structures. DPR and GMI-based Precipitation Features (PFs) parameters are used as proxies of the vertical structure and microphysical properties of these events, and their statistical distribution is analyzed to identify extremes. The analysis of annual, seasonal and geographical distribution of the identified deep convective systems highlights substantial differences in their diurnal cycle and in the distribution between land-sea and summer-winter. There is a general shift of the convective systems from the south (mostly over the sea) in the cold season, to the north (mostly over land) in the warm season. The analysis shows also that the inferred convective intensity is not always related to heavy precipitation. Known DPR and GMI-based criteria were adopted to identify overshooting top events and potential hailstorms, identify extreme deep convection signatures, like those observed for tropical and subtropical systems, and the most intense occur mostly over the sea. Although the analysis is limited to four years, the results show that the GPM-CO offers unprecedented measurements to identify and characterize extreme weather events in the Mediterranean region, with unique potentials for future long-term climatology and interannual variability analysis.