It is well known that scalar reaction-diffusion equations in homogeneous media admit special planar front solutions which propagate with a constant speed. They are stable for a large class of nonlinearities. Similar results have been established in periodic media by Berestycki and Hamel, and Weinberger. I will discuss generalizations of the notion of a traveling front to general heterogeneous media and, in particular, random media, as well as stability of those fronts when the nonlinearity is of the ignition type. This is ajoint work with J. Nolen, J.-M. Roquejoffe and A. Mellet.