The main attention is paid to the following questions: 1. The possible models of the luminescence centers in activated alkali halide crystals, 2. the experimental evidence of the presence of various types of the luminescence centers, 3. the nature of the excitations of the simplest luminescence centers in alkali halides activated by mercury-like ions and by some other ions. Mainly two possibilities of views: the “quasi-free ions” case on the one hand and the “quasi-molecular” models on the other are discussed in detail.