Abstract
The evolution of the inflationary theory is described, starting from the Starobinsky model and the old inflation scenario proposed by Guth, toward chaotic inflation and the modern theory of eternally expanding self- reproducing inflationary universe. A special attention is devoted to the recent progress in the theory of reheating after inflation. I describe also the recent development of inflationary cosmology with Ω ≠ 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 way to do it is to suggest a better cosmological theory.
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