Low counting experiments (search for double β decay and dark matter particles, measurements of neutrino fluxes from different sources, search for hypothetical nuclear and subnuclear processes, low background α, β, γ spectrometry) require extremely low background of a detector. Scintillators are widely used to search for rare events both as conventional scintillation detectors and as cryogenic scintillating bolometers. Radioactive contamination of a scintillation material plays a key role to reach low level of background. Origin and nature of radioactive contamination of scintillators, experimental methods and results are reviewed. A programme to develop radiopure crystal scintillators for low counting experiments is discussed briefly.