  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.
