The study of dynamical zeta functions is part of the theory of dynamical systems, but it is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. In the talk I will discuss dynamical zeta functions connected with Nielsen fixed point theory and describe congruences for the Reidemeister and Nielsen numbers. I will explain how dynamical zeta functions give rise to the Reidemeister torsion, an important topological invariant which has useful applications in knot theory, quantum field theory and dynamical systems.