The article summarizes achievements of E.I. Boiko's scientific school in their studies of physiological mechanisms of mental activity, analyzing the new approach to the solution of the psychophysiological problem formulated by the school and describing a new original method of analysing physiological mechanisms of human higher mental processes, data obtained with the help of the method and theoretical conclusions concerning brain organization of voluntary attention, selective perception, short-term memory, mental object comparison, voluntary motor responses to a verbal instruction. Findings of Boiko's school are analysed in the context of the problems of defining the subject-matter of psychology and the future of cognitive psychology.