  This paper is concerned with the existence and qualitative properties of
pulsating fronts for spatially periodic reaction-diffusion equations with
bistable nonlinearities. We focus especially on the influence of the spatial
period and, under various assumptions on the reaction terms and by using
different types of arguments, we show several existence results when the
spatial period is small or large. We also establish some properties of the set
of periods for which there exist non-stationary fronts. Furthermore, we prove
the existence of stationary fronts or non-stationary partial fronts at any
period which is on the boundary of this set. Lastly, we characterize the sign
of the front speeds and we show the global exponential stability of the
non-stationary fronts for various classes of initial conditions.
