  The survey is devoted to diverse applications of Besov classes in operator
theory. It is illustrated how Besov classes are used to describe Hankel
operators of Schatten--von Neumann classes; various applications of this
description are considered. Next, we discuss the role of Besov classes in norm
estimates of polynomials of power bounded operators on Hilbert space and
related estimates of Hankel matrices in tensor products of the spaces $\ell^1$
and $\ell^\infty$. An essential part of the survey is devoted to the role of
Besov spaces in various problems of perturbation theory when studying the
behavior of functions of a single operator or of a collection of operators
under their perturbation.
