In my talk, I will present our research activities on transport processes of interacting Bose-Einstein condensates in presence of dimensionally restricted disorder potentials. We study these processes by numerically integrating the Gross-Pitaevskii equation in presence of an external source that simulates the quasi-stationary injection of coherent matter waves onto the disorder region. For the case of one-dimensional disorder potentials, we find that the presence of the atom-atom interaction leads to a cross-over from an exponential to an algebraic decrease of the average transmission with the disorder length, which represents a significant deviation from the scenario of Anderson localization. For two-dimensional disorder potentials, the presence of interaction reverts the phenomenon of weak localization and leads to a cone-shaped dip, instead of a peak, in the angle-resolved current of backscattered atoms. Our numerical findings are corroborated by analytical approaches based, in the 1D case, on transfer-matrix-type methods and, in the 2D case, on nonlinear diagrammatic perturbation theory.