The interplay of disorder and electron interactions is in recent decade one of the most challenging theoretical problems in condensed-matter physics. It is interesting also in connection with experiments in real materials and cold gases on optical lattices. New paradigm is many-body localization, which predicts in systems with strong disorder the nonergodicity and absence of thermalization even in the presence of interaction, and appears to be realized in cold-atom systems. I will present some recent numerical results within the standard models of many-body localization, which confirm the existence of such a state, but I will show also limitations of this phenomenon.