This study aims at understanding how deep convection is organized and contributes to the intensification of nine Mediterranean tropical-like cyclones which developed between 2005 and 2018. Through a multi-satellite approach, a combination of infrared and microwave diagnostics provides insights into the temporal and spatial evolution of deep convection. ERA5 reanalysis complements the remote-sensing observations and is used to compute the vertical wind shear and vortex tilt to investigate their interactions with deep convection. Results show that vertical wind shear and topography have an important impact on the organization of deep convection and the symmetry of the cyclones. Only a fraction of these cyclones experienced intense convective activity close to their centres and we show that persistent deep convection in the upshear quadrants led to intensification periods. Convective activity solely in the downshear quadrants was not linked to intensification periods, while short-lived hurricane-like structures develop only during symmetric convective activity, leading to cyclone intensification in some of the cases. Finally, a classification of the Mediterranean tropical-like cyclones is proposed based on the evolution of deep convection and their intensification periods.