Abstract: The propagation of cosmic rays around sources is a complex phenomenon that involves the configuration of magnetic field lines and their level of turbulence. In addition, escaping CRs can trigger the excitation of plasma instabilities that enhance the residence time of the particles, while a variety of damping processes can suppress these instabilities. Such phenomena are very relevant for gamma-ray astronomy since they can affect the possible signal from molecular clouds located nearby CR accelerators, the chance of detecting Galactic Pevatrons, or the formation of gamma-ray halos around PWNe. Here we provide an overview of the main aspects related to the CR propagation around sources and their implications on gamma-ray observations and on CR observables.