Non-radiative transitions affect many aspects of semiconductor performance. Normally they reduce device efficiency by suppressing luminescence, creating defects, reducing carrier lifetimes, or enhancing diffusion during operation. The present review surveys both the theoretical and practical understanding of non-radiative transitions. It includes general theoretical results and the associated ideas, with the emphasis on phonon-induced and defect Auger processes. Most of the purely formal aspects are omitted, but the points of principle where uncertainties remain are discussed. The review also covers the relation between basic theoretical studies and practical applied work on device degradation. This includes a description of the atomic processes involved in the more important mechanism of device deterioration and the theoretical understanding of the mechanism of these underlying processes. Finally, there is a survey of models proposed for 'killer' centres.