The field of single-atom catalysis (SAC) has expanded greatly in recent years. While there has been much success developing new synthesis methods, a fundamental disconnect exists between most experiments and the theoretical computations used to model them. The real catalysts are based on powder supports, which inevitably contain a multitude of different facets, different surface sites, defects, hydroxyl groups, and other contaminants due to the environment. This makes it extremely difficult to determine the structure of the active SAC site using current techniques. To be tractable, computations aimed at modeling SAC utilize periodic boundary conditions and low-index facets of an idealized support. Thus, the reaction barriers and mechanisms determined computationally represent, at best, a plausibility argument, and there is a strong chance that some critical aspect is omitted. One way to better understand what is plausible is by experimental modeling, i.e., comparing the results of computations to experiments based on precisely defined single-crystalline supports prepared in an ultrahigh-vacuum (UHV) environment. In this review, we report the status of the surface-science literature as it pertains to SAC. We focus on experimental work on supports where the site of the metal atom are unambiguously determined from experiment, in particular, the surfaces of rutile and anatase TiO2, the iron oxides Fe2O3 and Fe3O4, as well as CeO2 and MgO. Much of this work is based on scanning probe microscopy in conjunction with spectroscopy, and we highlight the remarkably few studies in which metal atoms are stable on low-index surfaces of typical supports. In the Perspective section, we discuss the possibility for expanding such studies into other relevant supports.