The processing of dust in shocks in the interstellar medium can lead to changes in the dust to gas mass ratio and also to a radical evolution of the dust size distribution. Here we focus on the important results of numerical models that simulate the impact of shocks on the interstellar dust size distribution in molecular clouds and in the warm intercloud medium. We emphasize the necessity of detailed modelling of the grain charging processes and the grain inertia in order to unravel the complexities and consequences of the dust dynamics in shock waves.
