An understanding of the structure of catalytically active centers and the way in which they facilitate the progress of chemical reactions has come largely through the use of experimental techniques. During the past two decades, theoretical methods based on quantum chemistry, statistical mechanics, and absolute rate theory have advanced to a level where they can be used to confirm experimentally deduced structures of active centers and species adsorbed at such centers and to test hypotheses regarding the pathways by which catalyzed reactions proceed. Theoretical methods can also be used today to explore “what if” scenarios and to make suggestions for how to modify catalyst composition in order to achieve higher activity and selectivity. This talk will discuss briefly the theoretical tools that are currently available, and will illustrate their applications to several problems involving both homogeneous and heterogeneous catalysis. These illustrations will discuss the role of support composition on the activity of vanadate species for methanol oxidation to formaldehyde, the structure of molybdate species involved in the oxidation of methane to formaldehyde, the mechanism of oxidative carbonylation of methanol to dimethyl carbonate on Cu-Y, and the oxidative carbonylation of toluene to toluic acid.