Single-atom catalysts (SACs) hold great promise for maximizing atomic efficiency of supported metals via the ultimate utilization of every single atom. The foreign isolated substitutions anchored on different supports build varieties of local structural centers, changing the physical and chemical properties. Thus, distinct atomic local environments for single-atom catalysts are essential for determining superior catalytic performance for a wide variety of chemical reactions. The examples of synthesizing single atoms on various supports presented here deepen the understanding of the different structural and electronic properties of SACs, in which the metal single atom does not bind with any other atoms of this metal, but substantially interacts with the support ions. Due to the strong support effects, the ubiquitous aggregation of metal single atoms can be addressed, achieving highly stable SACs. This review discusses recent progress in theoretical electronic effects between atomic dopants and supports, which reveal the electronic structures of various SACs and offers guidance for rational prediction and design of highly stable and reactive SACs. It is argued that tuning this interaction by the selection of the supports toward favorable atomic and electronic structures on the surface should be taken into consideration for the development of more efficient SACs.