Some basic radiative and non-radiative processes taking place in semiconductor nanocrystals are discussed, and rates of these processes are calculated. In particular, in the present review we explore both intra-crystallite processes, such as the photon emission, Auger recombination, phononassisted exciton relaxation, capture on surface defects, multi-exciton generation, and inter-crystallite processes realized through the exciton migration in ensembles of nanocrystals. Exciton transitions, creation, and annihilation accompanied by the photon and (or) phonon emission or absorption are considered from the point of view of their influence on the optical properties of nanocrystals.