Some reaction-diffusion equations admit traveling wave
solutions, which are simple models of a chemical reaction spreading with
constant speed. Even in a heterogeneous medium, solutions to the initial
value problem may develop fronts propagating with a well-defined
asymptotic speed. I will describe recent progress in understanding how
fronts propagate in heterogeneous media. In particular, I will discuss
properties of generalized traveling waves for one-dimensional
reaction-diffusion equations with variable excitation. I also will
discuss multi-dimensional fronts in stationary ergodic random media.