Single-atom site catalysts (SASCs) are characterized with atomically dispersed isolated metal active sites and theoretically 100% metal dispersion. Supports with high specific surface area are crucial for the fabrication of highly efficient SASCs with maximized metal dispersion. The high specific surface area supports provide anchoring sites that stabilize the monodispersed active metal atoms. The metal atoms and their coordination environment jointly constitute the metal single-atom sites, which represent the active sites of SASCs. The selection of suitable supports is one of the key factors that determine the structures and properties of SASCs. In this perspective, we introduce various types of SASCs based on high specific surface area supports from 0-dimension to 3-dimension with different sorts of active sites and coordination environments. In particular, we select the most representative high specific surface supports in each dimension and introduce the corresponding SASCs and how different supports cooperate with single metal atoms to achieve efficient catalysis. We summarize the current developments, and also present future opportunities and challenges of SASCs, aiming to provide an instructive perspective of the SASCs based on high specific surface area supports.