Quantum cosmology at the turn of Millennium

A brief review of the modern state of quantum cosmology is presented as a theory of quantum initial conditions for inflationary scenario. The no-boundary and tunneling states of the Universe are discussed as a possible source of probability peaks in the distribution of initial data for inflation. It is emphasized that in the tree-level approximation the existence of such peaks is in irreconcilable contradiction with the slow roll regime -- the difficulty that is likely to be solved only on account of quantum gravitational effects. The low-energy (typically GUT scale) mechanism of quantum origin of the inflationary Universe with observationally justified parameters is presented for closed and open inflation models with a strong non-minimal coupling.