This review summarizes biobanks of umbilical cord blood (UCB), beginning with a series of crucial experiments to build the technology to treat hematological diseases. UCB is used as an alternative source of hematopoietic stem cells in the treatment of patients with hematological malignancies, bone marrow failure, and inherited metabolic abnormalities. In this review, we evaluate the procedures for collecting, processing, and storing cord blood and discuss the advantages and disadvantages of current applications in regenerative medicine, particularly for hematological disorders in Vietnam. Our analysis compares cord blood banks, including private and public banks, in Vietnam and worldwide. An integrative overview of UCB transplantation in patients with different diseases and the degree of patient adaptation is analyzed. This review concludes with an assessment of the impact of measures taken to combat the COVID-19 pandemic on the banking of autologous cord blood and cord tissue in Vietnam compared to other banks in the world. National policies in the fight against a pandemic may differ from the global level. Human behavior, access to medical treatment, number of health professionals, health facility infrastructure, and timing of response in different cultures contribute to these differences.