Recent advances in heterogeneous single-atom catalysts (SACs), which have isolated metal atoms dispersed on a support, have enabled a more precise control of their surface metal atomic structure. SACs could reduce the amount of metals used for the surface reaction and have often shown distinct selectivity, which the corresponding nanoparticles would not have. However, SACs typically have the limitations of low-metal content, poor stability, oxidic electronic states, and an absence of ensemble sites. In this review, various efforts to overcome these limitations have been discussed: The metal content in the SACs could increase up to over 10 wt %; highly durable SACs could be prepared by anchoring the metal atoms strongly on the defective support; metallic SACs are reported; and the ensemble catalysts, in which all the metal atoms are exposed at the surface like the SACs but the surface metal atoms are located nearby, are also reported. Metal atomic multimers with distinct catalytic properties have been also reported. Surface metal single-atoms could be decorated with organic ligands with interesting catalytic behavior. Heterogeneous atomic catalysts, whose structure is elaborately controlled and the surface reaction is better understood, can be a paradigm with higher catalytic activity, selectivity, and durability and used in industrial applications.