  This paper is concerned with transition fronts for reaction-diffusion
equations of the Fisher-KPP type. Basic examples of transition fronts
connecting the unstable steady state to the stable one are the standard
traveling fronts, but the class of transition fronts is much larger and the
dynamics of the solutions of such equations is very rich. In the paper, we
describe the class of transition fronts and we study their qualitative
dynamical properties. In particular, we characterize the set of their
admissible asymptotic past and future speeds and their asymptotic profiles and
we show that the transition fronts can only accelerate. We also classify the
transition fronts in the class of measurable superpositions of standard
traveling fronts.
