  In this review I briefly describe the evolution of the inflationary theory
from the scenario based on the idea of supercooling and expansion in the false
vacuum toward the theory of eternally expanding self-reproducing inflationary
universe. I describe recent development of inflationary cosmology with Omega <
1, and then discuss some issues related to the possibility to verify inflation
by comparing its predictions with observational data. I argue that it is
possible to verify and disprove many particular models of inflationary
cosmology, but it is very difficult to kill the basic idea of inflation. It
seems that the best (and may be even the only) way to do so is to suggest a
better cosmological theory.
