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