The historical, lexical and conceptual issues embedded in stem cell biology are reviewed from technical, ethical, philosophical, judicial, clinical, economic and biopolitical perspectives. The mechanisms assigning the simultaneous capacity to self-renew and to differentiate to stem cells (immortal template DNA and asymmetric division) are evaluated in the light of the niche hypothesis for the stemness state. The induction of cell pluripotency and the different stem cells sources are presented (embryonic, adult and cord blood). We highlight the embryonic and adult stem cell properties and possible therapies while we emphasize the particular scientific and social values of cord blood donation to set up cord blood banks. The current scientific and legal frameworks of cord blood banks are reviewed at an international level as well as allogenic, dedicated and autologous donations. The expectations and the challenges in relation to present-day targeted diseases like diabetes mellitus type 1, Parkinson's disease and myocardial infarction are evaluated in the light of the cellular therapies for regenerative medicine.