Adipose stromal/stem cells (ASCs) are an ideal cell type for regenerative medicine applications, as they can easily be harvested from adipose tissue in large quantities. ASCs have excellent proliferation, differentiation, and immunoregulatory capacities that have been demonstrated in numerous studies. Great interest and investment have been placed in efforts to exploit the allogeneic use and immunomodulatory and anti-inflammatory effects of ASCs. However, bridging the gap between in vitro and in vivo studies and moving into clinical practice remain a challenge. For the clinical translation of ASCs, several issues must be considered, including how to characterise such a heterogenic cell population and how to ensure their safety and efficacy. This review explores the different phases of in vitro and preclinical ASC characterisation and describes the development of appropriate potency assays. In addition, good manufacturing practice requirements are discussed, and cell-based medicinal products holding marketing authorisation in the European Union are reviewed. Moreover, the current status of clinical trials applying ASCs and the patent landscape in the field of ASC research are presented. Overall, this review highlights the applicability of ASCs for clinical cell therapies and discusses their potential.