Effective transport properties for diffusion in random media

Results on the calculation of the long time self-diffusion constant of a Brownian particle in a random environment are reviewed. We concentrate on the case of diffusion in a force field generated by a quenched random potential and the case of diffusion in an environment with a quenched, spatially varying, random diffusivity. Mathematical relations between these two problems and exact results in low dimensions are discussed as well as approximative perturbation schemes for these computations. Numerical techniques used in the simulation of these systems are also discussed.