Despite many successes in synthesizing single-atom catalysts, there is a fundamental mismatch between most experimental work and the theoretical modelling of these systems. Applied catalysts are based on complex powder supports and are fabricated and used in environments containing various potential ligands and contaminants, whereas theoretical treatment is generally based on density functional theory (DFT) calculations assuming low-index facets on idealized supports, often placing the single catalyst atom in a bulk continuation site. Single-crystal supports prepared in UHV provide a direct experimental analogue to DFT and a bridge to more complex systems, enabling validation of the sites assumed by theory. Using the iron oxide α-Fe2O3 as an example, I will show that simple adatom or substitutional models are generally not representative of the structures found in surface-science experiments. Stabilization requires added complexity, such as dynamic surface restructuring and stabilizing ligands from the gas phase. These factors must be taken into account to explain the experimental data. I will summarize recent results on dispersed Rh and Pt atoms on the α-Fe2O3(11 ̅02) facet, outline our current theoretical picture, and highlight preliminary findings and open challenges for both experiment and modelling.