Regenerative dental medicine continuously expands to improve treatments for prevalent clinical problems in dental and oral medicine. Stem cell based translational opportunities include regenerative therapies for tooth restoration, root canal therapy, and inflammatory processes (e.g., periodontitis). The potential of regenerative approaches relies on the biological properties of dental stem cells. These and other multipotent somatic mesenchymal stem cell (MSC) types can in principle be applied as either autologous or allogeneic sources in dental procedures. Dental stem cells have distinct developmental origins and biological markers that determine their translational utility. Dental regenerative medicine is supported by mechanistic knowledge of the molecular pathways that regulate dental stem cell growth and differentiation. Cell fate determination and lineage progression of dental stem cells is regulated by multiple cell signaling pathways (e.g., WNTs, BMPs) and epigenetic mechanisms, including DNA modifications, histone modifications, and non-coding RNAs (e.g., miRNAs and lncRNAs). This review also considers a broad range of novel approaches in which stem cells are applied in combination with biopolymers, ceramics, and composite materials, as well as small molecules (agonistic or anti-agonistic ligands) and natural compounds. Materials that mimic the microenvironment of the stem cell niche are also presented. Promising concepts in bone and dental tissue engineering continue to drive innovation in dental and non-dental restorative procedures.