  In this talk we discuss three different issues. First of all, there exist
several proposals how to solve cosmological problems by adiabatic expansion of
the Universe, without any use of inflation. We explain why these models do not
solve the flatness/entropy problem. On the other hand there exist some claims
that inflation also does not solve the flatness problem. We show that these
claims are correct to a certain extent for old and new inflation, but are
incorrect for simplest versions of chaotic inflation. The second issue to be
considered is the classification of inflationary models. At present many
inflationary models are compared to each other in order to understand which of
them better describes observational data. Unfortunately, this often leads to
terminological misunderstandings and even to misleading conclusions. We discuss
three coexisting types of classification of inflationary models and explain
their relation to each other. We also briefly describe the hybrid inflation
model, which combines several interesting features of different inflationary
models. Finally we show that it is possible to describe inflationary universe
by a stationary (i.e. time-independent) probability distribution to find a
domain of a given size containing matter with given properties. This represents
a strong deviation of inflationary cosmology from the standard Big Bang
paradigm.
