There are strong economic forces that demand rational methods for the development of new catalysts. A basis for the solution of this problem are appropriate models of the phenomena within catalyst supports, augmented with a wide variety of experimental methods. This paper deals with models of the porous structures of catalyst supports, multi-component diffusion, chemisorption, reaction, desorption and deactivation. Mathematical methods of quantum chemistry and statistical physics will be briefly described. The powerfulness of modern modelling approaches will especially be demonstrated with zeolites.