The investigations of the properties of quantum chaos in the simple models, such as kicked rotator, allowed to understand the quantum picture of microwave ionization of highly excited hydrogen atoms. The predicted effect of quantum localization of chaos for hydrogen atom in a microwave field was observed in the experiments of Bayfield and Koch. The phenomenon of such unusual diffusive photoelectric effect, in which direct one-photon ionization is much less effective than the ionization at much smaller frequency, was explained on the grounds of the theory of quantum localization of classical chaos and Kepler map (main refs.[13,15,17,26,33]). This problem is the first real physical system in which dynamical localization of quantum chaos has been observed in a laboratory. Recently, dynamical localization was observed in experiments with cold atoms by Raizen et al. (see section 3.5.3).