Considered a total social phenomenon, mobility is at the center of intricate social dynamics in cities and serves as a reading lens to understand the whole society. With the advent of big data, the potential for using mobility as a key social analyzer was unleashed in the past decade. The purpose of this research is to systematically review the evolution of big data's role in revealing social dimensions of urban mobility and discuss how they have contributed to various research domains from early 2010s to now. Six major research topics are detected from the selected online academic corpuses by conducting keywords-driven topic modeling techniques, reflecting diverse research interests in networked mobilities, human dynamics in spaces, event modeling, spatial underpinnings, travel behaviors and mobility patterns, and sociodemographic heterogeneity. The six topics reveal a comprehensive, research-interests, evolution pattern, and present current trends on using big data to uncover social dimensions of human mobility activities. Given these observations, we contend that big data has two contributions to revealing social dimensions of urban mobility: as an efficiency advancement and as an equity lens. Furthermore, the possible limitations and potential opportunities of big data applications in the existing scholarship are discussed. The review is intended to serve as a timely retrospective of societal-focused mobility studies, as well as a starting point for various stakeholders to collectively contribute to a desirable future in terms of mobility.