The contradictions characteristic for testological and experimental-psychological approaches to the study of Intellect and resulting in the illusion of its "disappearance" as of real psychic capacity are considered. The necessity to analyse the structural organization of intellect is stressed. Three problems connected to it are discussed: what is the nature of cognitive psychic structures being the foundation of human intellect functioning; what are the properties of Individual Intellect cognitive space organization; what is the specificity of reality's intellectual representations.