The article presents the problem of improving cognitive deficits through cognitive training. A definition of cognitive training is given. Effectiveness of cognitive training is discussed, especially whether trainig can induce objectively observable brain changes. A review of contemporary studies of cognitive training done at Lomonosov MSU and Institute of Cognitive Studies (RNC "Kurchatov'S Institute") is given. Results of computational experiments are presented, which point at the effectiveness of special procedures of adaptive training and at the effectiveness of new methods for registering weak brain changes induced by training.