Dark matter self-interactions are frequently put forward in the explanation of small structure problems in the universe. They could have important implications on the formation and evolution of structures, from dwarf galaxies to large galaxy clusters. In this thesis, the effects of bremsstrahlung in self-interacting dark matter collisions on structure formation are analyzed. For that purpose, four different dark matter models are studied perturbatively in a non-relativistic and non-degenerate limit. Cross sections and energy loss rates are calculated analytically for all models for vanishing masses of the mediator and emitted particle and numerically for finite masses. To analyze the effect of radiative cooling on structure formation, the cooling time of a gas of dark matter particles, based on perturbative calculations, is compared to the elastic scattering time scale, the Hubble time and the gravitational timescale.