Three central questions have emerged in nanoscale heterogeneous catalysis: First, how does the structure and catalytic function of transition metal catalysts evolve as particles decrease in size from the micro to the nanoscale? Second, how do these particles interact and communicate with supports, and what are the effects on structure and reactivity? Third, how does the particle/support system respond to realistic and dynamic reaction environments? In this work we use first-principles density functional theory methods to consider these three questions in the context of oxidation catalysis on 1-10 atom Pt clusters. Using DFT-parameterized thermodynamic models, we explore the structure and compostion of the clusters as a function of oxidation conditions, illustrating the pronounced tendency to become partially to completely oxidized under most practically relevant conditions.@footnote 1@ This tendency is shown to persist but to be modified in clusters supported on an undefected MgO surface. To probe the consequences of environment and support on reactivity, we constrast the reactivity of the clusters toward strong (CO) and weak (NO) reductants. The results illustrate that both particle size and reactive environment can have a signficant influence on the reactivity of metal clusters and start to clarify the origins of these effects. @FootnoteText@ @footnote 1@ Y. Xu, W. A. Shelton, and W. F. Schneider, "Effect of Particle Size on the Oxidizability of Platinum Clusters," J. Phys. Chem. A, 2006, in press.