Non-linear MHD simulations of ELMs show features that are in good qualitative agreement with experimental observations. The formation of density filaments are due to the ballooning mode convection wheras the sub-structure in the heat deposition profile on the divertor target is dominated by the magnetic field perturbation of the ballooning instability. A first study of the ELM size as a function of collisionality shows an increasing ELM size with decreasing collisionality but only in the 'ideal' MHD regime. The increased losses at lower collisionality are due to the larger parallel heat conduction: the change in the temperature profile increases whereas the convected density losses do not vary with decreasing collisionality. MHD simulations of pellets 'injected' in an H-mode pedestal can lead to the destabilisation of a ballooning mode due to the high pressure in the pellet cloud for pellet larger than a critical pellet size. In x-point plasmas, the nonlinear MHD simulations indicate a partial direct loss of the pellet density when the pellet cloud arrives at the xpoint. This results in a single spiral in the target heat deposition profile, similar to what has been observed in JET experiments. This structure expands in the toroidal direction with the pellet cloud expanding with the local sound speed.