  This paper is chiefly concerned with qualitative properties of some
reaction-diffusion fronts. The recently defined notions of transition fronts
generalize the standard notions of traveling fronts. In this paper, we show the
existence and the uniqueness of the global mean speed of bistable transition
fronts in R^N. This speed is proved to be independent of the shape of the level
sets of the fronts. The planar fronts are also characterized in the more
general class of almost-planar fronts with any number of transition layers.
These qualitative properties show the robustness of the notions of transition
fronts. But we also prove the existence of new types of transition fronts in
R^N that are not standard traveling fronts, thus showing that the notions of
transition fronts are broad enough to include other relevant propagating
solutions.
