The fundamental limits on the scintillation decay, scintillation yield, and X-ray or gamma-ray energy resolution obtainable with Ce3+, Pf(3+), and Eu2+ activated inorganic scintillators are determined. Those limits are compared with what has been achieved today with scintillators like YAlO3:Ce, Lu2SiO5:Ce, LaCl3:Ce, LaBr3:Ce, LuI3:Ce, and emerging scintillators like Lu3Al5O12:Pr3+ and SrI2:Eu2+. Higher scintillation yield not necessarily leads to better energy resolution; nonproportional scintillation yield with deposited amount of ionization energy is an important aspect too that will be addressed.