Atomically dispersed heterogeneous catalysts offer the opportunity to design active sites with molecular precision. A recent proliferation of synthetic strategies and advanced characterization tools has propelled broad interest in leveraging these catalysts in diverse areas of chemistry beyond thermal heterogeneous catalysis, including but not limited to organic synthesis, electrochemistry, photochemistry and environmental chemistry. This Perspective aims to arm researchers in this area with the methodological framework and fundamental principles to accurately assess the degree of uniformity of heterogeneous catalyst active sites, and to link the synthesis, structure and function of atomically dispersed catalysts to one another. A paedagogical discussion of catalyst structural dynamics and active-site-specific characterization is supplemented with recent case studies that illustrate these fundamentals. This analysis shows how progress can be guided by requiring that the characterization of active sites is connected to their kinetic behaviour in the form of turnover rates and by leveraging the thermokinetic factors that control active site structures and their dynamics.