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The paper is devoted to fundamental problems of the Wheeler - DeWitt quantumgeometrodynamics, which was the first attempt to apply quantum principles tothe Universe as a whole. Our purpose is to find out the origin of theseproblems and follow up their consequences. We start from Dirac generalizedHamiltonian dynamics as a cornerstone on which the Wheeler - DeWitt theory isbased. We remind the main statements of the famous DeWitt's paper of 1967 anddiscuss the flaws of the theory: the well-known problem of time, the problem ofHilbert space and others. In the concluding part of the paper we consider newtendencies and approaches to quantum geometrodynamics appeared in the lastdecade.

The Wheeler - DeWitt Quantum Geometrodynamics: its fundamental problems and tendencies of their resolution