This second part of the review deals with the pore structures of catalyst supports. Starting with the simple parallel-bundle model, the models developed by Butt and Foster, Johnson and Stewart or Wakao and Smith, we proceed to sophisticated three-dimensional lattice models. Deactivation by coking etc. is described by percolation theory. Fractals are used to characterize the details of catalyst surfaces. Finally, it is demonstrated the potentiality of computeraided catalyst design, especially the optimization of catalyst distribution and pore size optimization. The status of technical realization of optimum pore structures will be discussed.