  In this paper we consider a bistable reaction-diffusion equation in unbounded
domains and we investigate the existence of propagation phenomena, possibly
partial, in some direction or, on the contrary, of blocking phenomena. We start
by proving the well-posedness of the problem. Then we prove that when the
domain has a decreasing cross section with respect to the direction of
propagation there is complete propagation. Further, we prove that the wave can
be blocked as it comes to an abrupt geometry change. Finally we discuss various
general geometrical properties that ensure either partial or complete invasion
by 1. In particular, we show that in a domain that is "star-shaped" with
respect to an axis, there is complete invasion by 1.
