To approach a microscopic understanding of the reaction kinetics on complex surfaces of heterogeneous catalysts, we combine multimolecular beam techniques and a supported model catalyst approach. The model systems are prepared under ultrahigh vacuum (UHV) conditions and have been characterized in detail with respect to their geometric and electronic structure. To probe the kinetics of catalytic reactions on these systems, we have developed a molecular beam instrument, which allows us to cross up to three beams on the sample surface. The simultaneous detection of reaction products and surface species is established by a combination of angle- and time-resolved gas-phase detection and in situ time-resolved IR reflection absorption spectroscopy. In this paper, we review a variety of representative experiments, illustrating the experimental possibilities of the molecular beam approach. As a model surface, we focus on alumina supported palladium particles. We cover the adsorption and desorption kinetics of small molecules and the kinetics of simple surface reactions on these systems. The reaction kinetics is probed via systematic steady state measurements, transient experiments, time-resolved in situ IR spectroscopy and measurements of the angular distribution of products. A central topic is. the CO oxidation, a model reaction, which has been thoroughly investigated on a variety of single crystal surfaces. For the supported model catalysts, it is shown how structure and size dependencies can be identified by performing systematic kinetic measurements. These effects can be linked to the inherent heterogeneity of the model surfaces via microkinetic mean-field and Monte Carlo simulations. It is shown that the particular kinetic effects on the model catalyst surfaces can be understood by explicitly accounting for their inherent complexity. Finally, we outline possible future directions of the molecular beam approach applied to complex model surfaces.