The propagation of particles in random backgrounds is of interest from several points of view. Disordered media is one but my own originates in discretized quantum gravity. I will discuss some of the background and the motivation for this. Recently there has been considerable progress in obtaining essentially exact results for some problems of this type. The methods are actually very simple and intuitive and I'll explain how they work. Finally there are of course many open problems still and I'll close with them.