Toxic, viral and surgical injuries can pose medical indications for liver transplantation. The number of patients waiting for a liver transplant still increases, but the number of organ donors is insufficient. Hepatocyte transplantation was suggested as a promising alternative to liver transplantation, however, this method has some significant limitations. Currently, afterbirth tissues seem to be an interesting source of cells for the regenerative medicine, because of their unique biological and immunological properties. It has been proven in experimental animal models, that the native stem cells, and to a greater extent, hepatocyte-like cells derived from them and transplanted, can accelerate regenerative processes and restore organ functioning. The effective protocol for obtaining functional mature hepatocytes in vitro is still not defined, but some studies resulted in obtaining functionally active hepatocyte-like cells. In this review, we focused on human stem cells isolated from placenta and umbilical cord, as potent precursors of hepatocyte-like cells for regenerative medicine. We summarized the results of preclinical and clinical studies dealing with the introduction of epithelial and mesenchymal stem cells of the afterbirth origin to the liver failure therapy. It was concluded that the use of native afterbirth epithelial and mesenchymal cells in the treatment of liver failure could support liver function and regeneration. This effect would be enhanced by the use of hepatocyte-like cells obtained from placental and/or umbilical stem cells.