This article is a review of the physical characterization of well-defined site-isolated molecular metal complexes and metal clusters supported on metal oxides and zeolites. These surface species are of interest primarily as catalysts; as a consequence of their relatively uniform structures, they can be characterized much more precisely than traditional supported catalysts. The properties discussed in this review include metal nuclearity, oxidation state, and ligand environment, as well as metal-support interactions. These properties are determined by complementary techniques, including transmission electron microscopy; X-ray absorption, infrared, Raman, and NMR spectroscopies; and density functional theory. The strengths and limitations of these techniques are assessed in the context of results characterizing samples that have been investigated thoroughly and with multiple techniques. The depth of understanding of well-defined metal complexes and metal clusters on supports is approaching that attainable for molecular analogues in solution. The results provide a foundation for understanding the more complex materials that are typical of industrial catalysts.