  In this chapter we review concepts and theories of polymer dynamics. We think
of it as an introduction to the topic for scientists specializing in other
subfields of statistical mechanics and condensed matter theory, so, for the
readers reference, we start with a short review of the equilibrium static
properties of polymer systems. Most attention is paid to the dynamics of
unentangled polymer systems, where apart from classical Rouse and Zimm models
we review some recent scaling and analytical generalizations. The dynamics of
systems with entanglements is also briefly reviewed. Special attention is paid
to the discussion of comparatively weakly understood topological states of
polymer systems and possible approaches to the description of their dynamics.
