This dissertation is focused on understanding the structure-activity relationship in heterogeneous catalysis by studying model catalytic systems. The catalytic oxidation of CO was chosen as a model reaction for studies on a variety of catalysts. A series of Au/TiO2 catalysts were prepared from various metalorganic gold complexes. The catalytic activity and the particle size of the gold catalysts were strongly dependent on the gold complexes. The Au/TiO2 catalyst prepared from a tetranuclear gold complex showed the best performance for CO oxidation, and the average gold particle size of this catalyst was 3.1 nm. CO oxidation was also studied over Au/MgO catalysts, where the MgO supports were annealed to various temperatures between 900 and 1300 K prior to deposition of Au. A correlation was found between the activity of Au clusters for the catalytic oxidation of CO and the F-center concentration in the MgO support. In addition, the catalytic oxidation of CO was studied in a batch reactor over supported Pd/Al2O3 catalysts, a Pd(100) single crystal, as well as polycrystalline metals of rhodium, palladium, and platinum. A hyperactive state, corresponding to an oxygen covered surface, was observed at high O2/CO ratios at elevated pressures. The reaction rate at this state was significantly higher than that on CO-covered surfaces at stoichiometric conditions. The oxygen chemical potential required to achieve the hyperactive state depends on the intrinsic properties of the metal, the particle size, and the reaction temperature. A well-ordered ultra-thin titanium oxide film was synthesized on the Mo(112) surface as a model catalyst support. Two methods were used to prepare this Mo(112)- (8x2)-TiOx film, including direct growth on Mo(112) and indirect growth by deposition of Ti onto monolayer SiO2/Mo(112). The latter method was more reproducible with respect to film quality as determined by low-energy electron diffraction and scanning tunneling microscopy. The thickness of this TiOx film was one monolayer and the oxidation state of Ti was +3 as determined by Auger spectroscopy, high-resolution electron energy loss spectroscopy, and X-ray photoelectron spectroscopy.