ConspectusTo improve the reactivity of catalysts, two goals that are perhaps the most obvious but at the same time the most elusive ones are (1) to increase the number of active sites and/or (2) to enhance the intrinsic activity of each active site. Both seem realizable in single-atom catalysts (SACs), in which in principle all of the metal sites could be active sites. The enhanced reactivity of SACs and their unique reaction mechanisms originate from their unique structures and interactions with supports. The details of these structures are therefore the focus of intense investigation and debates. Among the factors hindering the progress in their investigation is the complexity of SAC systems, which is primarily related to the heterogeneity in their structures within the same sample. In this Account, we outline strategies that we have found to be useful for selected systems we have studied that can also be applied to many other SACs.As an example of the most uniformly distributed SAC system, we focus on a Pt SAC support on nanoceria. A combination of imaging and spectroscopic techniques confirmed the atomic dispersion of Pt and the uniform distribution of Pt2+ single-atom sites. That uniformity was a prerequisite for determining the three-dimensional structure of Pt single atoms on the support surface. Our work illuminated the dependence of the structure and dynamics of Pt single atoms on the type of support. For Pt/ceria SACs, upon breaking of the Pt-O-Ce interaction at high temperatures under reductive conditions, the SACs aggregated into Pt nanoparticles that were active for the water gas shift reaction. In contrast, when Pt single atoms were anchored on the surface of a Co3O4 support, the removal of O in H2 at high temperatures resulted in the formation of Pt1Com/Co3O4 single-atom alloys (SAAs), which showed high N2 selectivity for NO reduction. In SAAs with increased complexity, when the interparticle distribution of compositions of catalytically active species is narrow, advanced methods of X-ray absorption near-edge structure (XANES) analysis, e.g., those employing machine learning, allow their placements within "representative" particles to be deciphered and their changes in reaction conditions to be tracked.Increasing the level of heterogeneity in the binding sites available to SACs blurs the resolution of spectroscopic methods such as X-ray absorption fine structure (XAFS) spectroscopy for detecting the details of their environments. We illustrate the effects of heterogeneity of the distribution of singly dispersed metal active sites using the PtNi/SBA-15 bimetallic catalyst as an example. In this system, the fact that Ni atoms existed in two types of species (the silicate phase and the PtNi nanoclusters) complicated the XAFS analysis, although when corrections for the silicate phase were applied, the results obtained from extended XAFS (EXAFS) data analysis helped to determine the three-dimensional structure of the PtNi nanoclusters.While not a review of the field, this Account is aimed to share with the readers our efforts to resolve challenges due to many forms of structural complexity existing in most heterogeneous single-atom systems and obtain insights into the unique atomic structures, as inferred from the correlative use of multimodal characterization tools and advances in data analysis and modeling methods that we developed.