  In this review I consider several different issues related to inflation. I
will begin with the wave function of the Universe. This issue is pretty old,
but recently there were some new insights based on the theory of the
self-reproducing inflationary universe. Then we will discuss stationarity of
inflationary universe and the possibility to make predictions in the context of
quantum cosmology using stochastic approach to inflation. Returning to more
pragmatic aspects of inflationary theory, we will discuss inflationary models
with $\Omega < 1$. Finally, we will describe several aspects of the theory of
reheating of the Universe based on the effect of parametric resonance.
