  We give a discussion of the classical Bowen$\unicode{x2013}$Series coding
and, in particular, its application to the study of zeta functions and their
zeros. In the case of compact surfaces of constant negative curvature $-1$ the
analytic extension of the Selberg zeta function to the entire complex plane is
classical, and can be achieved using the Selberg trace formula. However, an
alternative dynamical approach is to use the Bowen$\unicode{x2013}$Series
coding on the boundary at infinity to obtain a piecewise analytic expanding map
from which the extension of the zeta function can be obtained using properties
of the associated transfer operator. This latter method has the advantage that
it also applies in the case of infinite area surfaces provided they do not have
cusps. For such examples the location of the zeros is somewhat more mysterious.
However, in particularly simple examples there is a striking structure to the
zeros when we take appropriate limits. We will try to give some insight into
this phenomenon.
  The survey is based on lectures given by the first author during the Workshop
on Statistical Properties of Nonequilibrium Dynamical Systems which took place
in July 2016 at South University of Science and Technology of China in
ShenZhen.
