The usual notions of reaction-diffusion waves or fronts can be viewed as examples of generalized transition waves. These new notions involve uniform limits, with respect to the geodesic distance, to a family of hypersurfaces which are parametrized by time. The existence of transition waves has been proved in various contexts where the standard notions of waves make no sense anymore. In this talk, I will focus on some uniqueness and further qualitative properties of the transition waves, including the existence and uniqueness of the mean speed for somes classes of equations. The talk is also based on some joint works with H. Berestycki and H. Matano.