The present work is devoted to the investigation of oxidation reactions over RuO2 surfaces. Two main points are addressed. First, on the fundamental level, a detailed investigation of the site requirement for CO (as well as for methanol) and O-2 adsorption on the surface of a well-defined RuO2(110) crystal is conducted. Second, a comparison with polycrystalline RuO2 toward these oxidation reactions is presented. Both results, those in UHV over RuO2 (110) and those at atmospheric pressure over polycrystalline RuO2, agree fairly well. This indicates that the surface chemistry of the (110) single crystal is very similar to that of the polycrystalline material. Both the activity of the RuO2(110) surface in the UHV regime and the activity of polycrystalline RuO2 in the high-pressure regime were investigated by temperature-programmed desorption and by X-ray photoelectron spectroscopy. The reasons for the unusually high catalytic activity for oxidation reactions of RuO2 are traced back to the strong bonding of the reactants over the undercoordinated Ru atoms together with the presence of weakly bound undercoordinated oxygen species, serving as the oxidizing agent.