Medical research in regenerative medicine and cell-based therapy has brought encouraging perspectives for the use of stem cells in clinical trials. Multiple types of stem cells, from progenitors to pluripotent stem cells, have been investigated. Among these, dental pulp stem cells (DPSCs) are mesenchymal multipotent cells coming from the dental pulp, which is the soft tissue within teeth. They represent an interesting adult stem cell source because they are recovered in large amount in dental pulps with non-invasive techniques compared to other adult stem cell sources. DPSCs can be obtained from discarded teeth, especially wisdom teeth extracted for orthodontic reasons. To shift from promising preclinical results to therapeutic applications to human, DPSCs must be prepared in clinical grade lots and transformed into advanced therapy medicinal products (ATMP). As the production of patient-specific stem cells is costly and time-consuming, allogenic biobanking of clinical grade human leukocyte antigen (HLA)-typed DPSC lines provides efficient innovative therapeutic products. DPSC biobanks represent industrial and therapeutic innovations by using discarded biological tissues (dental pulps) as a source of mesenchymal stem cells to produce and store, in good manufacturing practice (GMP) conditions, DPSC therapeutic batches. In this review, we discuss about the challenges to transfer biological samples from a donor to HLA-typed DPSC therapeutic lots, following regulations, GMP guidelines and ethical principles. We also present some clinical applications, for which there is no efficient therapeutics so far, but that DPSCs-based ATMP could potentially treat.