Kolmogorov and linear diameters of functional classes and finite dimensional sets

In this paper we give a brief review of results concerning the Kolmogorov and linear diameters of Sobolev, Holder-Nikol'skii and Besov classes of periodic functions of one and several variables as well as of finite-dimensional sets. We present theorems for the order estimates of diameters obtained by the author, Temlyakov and others.