Semiconductor scintillators are worth studying because they include both the highest luminosities and shortest decay times of all known scintillators. Moreover, many semiconductors have the heaviest stable elements (Tl, Hg, Pb, Bi) as a major constituent and a high ion pair yield that is proportional to the energy deposited. We review the scintillation properties of semiconductors activated by native defects, isoelectronic impurities, donors and acceptors with special emphasis on those that have exceptionally high luminosities (e.g. ZnO:Zn, ZnS:Ag,Cl, CdS:Ag,Cl) and those that have ultra-fast decay times (e.g. ZnO:Ga; CdS:In). We discuss underlying mechanisms that are consistent with these properties and the possibilities for achieving (1) 200,000 photons/MeV and 1% fwhm energy resolution for 662 keV gamma rays, (2) ultra-fast (ns) decay times and coincident resolving times of 30 ps fwhm for time-of-flight positron emission tomography, and (3) both a high luminosity and an ultra-fast decay time from the same scintillator at cryogenic temperatures.