Recent advances in the synthesis and characterization of small, essentially molecular metal complexes and metal clusters on support surfaces have brought new insights to catalysis and point the way to systematic catalyst design. We summarize recent work unraveling effects of key design variables of site-isolated catalysts: the metal, metal nuclearity, support, and other ligands on the metals, also considering catalysts with separate, complementary functions on supports. The catalysts were synthesized with the goal of structural simplicity and uniformity to facilitate incisive characterization. Thus, they are essentially molecular species bonded to porous supports chosen for their high degree of uniformity; the supports are crystalline aluminosilicates (zeolites) and MgO. The catalytic species are synthesized in reactions of organometallic precursors with the support surfaces; the precursors include M(L)2(acetylacetonate)1-2, with M = Ru, Rh, Ir, or Au and the ligands L = C2H4, CO, or CH3. Os3(CO)12 and Ir4(CO)12 are used as precursors of supported metal clusters, and some such catalysts are made by ship-in-a-bottle syntheses to trap the clusters in zeolite cages. The simplicity and uniformity of the supported catalysts facilitate precise structure determinations, even in reactive atmospheres and during catalysis. The methods of characterizing catalysts in reactive atmospheres include infrared (IR), extended X-ray absorption fine structure (EXAFS), X-ray absorption near edge structure (XANES), and nuclear magnetic resonance (NMR) spectroscopies, and complementary methods include density functional theory and atomic-resolution aberration-corrected scanning transmission electron microscopy for imaging of individual metal atoms. IR, NMR, XANES, and microscopy data demonstrate the high degrees of uniformity of well-prepared supported species. The characterizations determine the compositions of surface metal complexes and clusters, including the ligands and the metal-support bonding and structure, which identify the supports as ligands with electron-donor properties that influence reactivity and catalysis. Each of the catalyst design variables has been varied independently, illustrated by mononuclear and tetranuclear iridium on zeolite HY and on MgO and by isostructural rhodium and iridium (diethylene or dicarbonyl) complexes on these supports. The data provide examples resolving the roles of the catalyst design variables and place the catalysis science on a firm foundation of organometallic chemistry linked with surface science. Supported molecular catalysts offer the advantages of characterization in the absence of solvents and with surface-science methods that do not require ultrahigh vacuum. Families of supported metal complexes have been made by replacement of ligands with others from the gas phase. Spectroscopically identified catalytic reaction intermediates help to elucidate catalyst performance and guide design. The methods are illustrated for supported complexes and clusters of rhodium, iridium, osmium, and gold used to catalyze reactions of small molecules that facilitate identification of the ligands present during catalysis: alkene dimerization and hydrogenation, H-D exchange in the reaction of H2 with D2, and CO oxidation. The approach is illustrated with the discovery of a highly active and selective MgO-supported rhodium carbonyl dimer catalyst for hydrogenation of 1,3-butadiene to give butenes.