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Two challenging scientific disciplines, i.e., the physics of glasses [Anderson, Science 267, 1615 (1995); Kennedy and Norman, Science 309, 75 (2005)] and interface chemistry [Sanders, 125 Questions: Exploration and Discovery (Science/AAAS, 2021); Yates and Campbell, Proc. Natl. Acad. Sci. U. S. A. 108, 911 (2011)], converge in research on the dynamics of glass surfaces. In recent decades, studies have revealed that glasses exhibit profound alterations in their dynamics within nanometers of interfaces. Rather, at the free surfaces of glassy materials with arrested bulk dynamics, a highly mobile ultrathin layer is present, wherein molecular mobility is much faster than in the bulk. Enhanced surface mobility has become an important scientific concept and is intrinsic and universal to various categories of glasses (e.g., molecular, metallic, and polymeric glasses), thus having technological implications for processing and applications of glasses. This review provides a comprehensive summary of the historical evolution of the concept, characterization, theoretical modeling, and unique features of dynamics at the surfaces of glasses. Additionally, this paper also illustrates potential advantages of incorporating this concept into designing improved materials with extraordinary properties. We hope this review article will contribute to the current understanding of the unique surface dynamics of glassy materials.