Transplantation of cord blood stem cells is a new and rapidly developing area. It has been used as a treatment for many diseases such as hematologic malignancies, primary immune deficiencies and metabolic diseases. Recently, stem cells have been used in regenerative medicine, particularly in neurodegenerative and cardiovascular diseases. For these reasons interest has been growing in banking cord blood. To be able to find an acceptable donor for any recipient in need, it is necessary to have on stock a great diversity of cells with different genetic types from different populations. Networks of banks and registries have been created around the world in order to share and exchange transplants. Public banks organize collection for altruistic donor of cord blood for unrelated hematopoietic stem cell transplantation and for directed donation in families at risk. But there are increasing numbers of families that are requesting storage of cord blood for possible future therapeutic use in the family. Establishment of cord blood banks has raised a number of important scientific, legal, ethical and political issues, which are discussed in this paper.