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The term ``sensitized luminescence'' in crystalline phosphors refers to the phenomenon whereby an impurity (activator, or emitter) is enabled to luminesce upon the absorption of light in a different type of center (sensitizer, or absorber) and upon the subsequent radiationless transfer of energy from the sensitizer to the activator. The resonance theory of Förster, which involves only allowed transitions, is extended to include transfer by means of forbidden transitions which, it is concluded, are responsible for the transfer in all inorganic systems yet investigated. The transfer mechanisms of importance are, in order of decreasing strength, the overlapping of the electric dipole fields of the sensitizer and the activator, the overlapping of the dipole field of the sensitizer with the quadrupole field of the activator, and exchange effects. These mechanisms will give rise to ``sensitization'' of about 103−104, 102, and 30 lattice sites surrounding each sensitizer in typical systems. The dependence of transfer efficiency upon sensitizer and activator concentrations and on temperature are discussed. Application is made of the theory to experimental results on inorganic phosphors, and further experiments are suggested.