The kinetics of vitrification of glass forming melts and the subsequent evolution of the frozen-in structure of the glass, i.e. the process of its stabilization, are usually described in the framework of thermodynamics of irreversible processes. Such a phenomenological approach has great advantages. However, by its very physical nature it cannot give a molecular interpretation of the changes taking place during vitrification and stabilization. That is why in the present contribution atomistic approaches describing the kinetics of stabilization of glasses, based on lattice-hole models of simple and polymer liquids are analyzed. Thus, the problems of the kinetics of stabilization of glasses are redefined in a new atomistic approach.