  We present a survey of results related to the Milnor's problem on group
growth. We discuss the cases of polynomial growth, exponential but not
uniformly exponential growth, but the main part of the article is devoted to
the intermediate (between polynomial and exponential) growth case. A number of
related topics (growth of manifolds, amenability, asymptotic behavior of random
walks) is considered, and a number of open problems is suggested.
