Umbilical cord blood (UCB) and, more recently, umbilical cord tissue (UCT) have been stored cryopreserved in private and public cord blood and tissue banks worldwide, since the umbilical cord blood was used for the first time in a child with Fanconi anemia with his HLA-identical sibling, following strict guidelines that imply high-quality standards and total rastreability of these units. The hematopoietic stem cells (HSCs) are clinically used in hematopoietic treatments for blood disorders and hemato-oncological diseases. Also, the mesenchymal stem cells (MSCs) isolated from the UCT and UCB, nowadays, can be used as coadjuvants of hematopoietic transplants. In the near future, these stem cells will have a crucial role in regenerative medicine. For this reason, these cells have been tested in several clinical trials and compassive treatments in children and adults, concerning a wide range of pathologies and diseases, for instance, for the treatment of cerebral paralysis. Considering the worldwide availability of UCB and UCT units and the absence of ethical concerns will probably become the best sources for cell-based therapies for hematological and nonhematological pathologies. The UCB will also have a crucial role in neonatology-predictive analysis in the near future.