Human dental pulp stem/stromal cells (hDPSCs) derived from the permanent secondary dentition are recognised to possess certain advantageous traits, which support their potential use as a viable source of mesenchymal stem/stromal cells (MSCs) for regenerative medicine-based applications. However, the well-established heterogeneous nature of hDPSC subpopulations, coupled with their limited numbers within dental pulp tissues, has impeded our understanding of hDPSC biology and the translation of sufficient quantities of these cells from laboratory research, through successful therapy development and clinical applications. This article reviews our current understanding of hDPSC biology and the evidence underpinning the molecular basis of their heterogeneity, which may be exploited to distinguish individual subpopulations with specific or superior characteristics for regenerative medicine applications. Pertinent unanswered questions which still remain, regarding the developmental origins, hierarchical organisation, and stem cell niche locations of hDPSC subpopulations and their roles in hDPSC heterogeneity and functions, will further be explored. Ultimately, a greater understanding of how key features, such as specific cell surface, senescence and other relevant genes, and protein and metabolic markers, delineate between hDPSC subpopulations with contrasting stemness, proliferative, multipotency, immunomodulatory, anti-inflammatory, and other relevant properties is required. Such knowledge advancements will undoubtedly lead to the development of novel screening, isolation, and purification strategies, permitting the routine and effective identification, enrichment, and expansion of more desirable hDPSC subpopulations for regenerative medicine-based applications. Furthermore, such innovative measures could lead to improved cell expansion, manufacture, and banking procedures, thereby supporting the translational development of hDPSC-based therapies in the future.