The incidence of liver disease is increasing globally. The only curative therapy for severe end-stage liver disease, liver transplantation, is limited by the shortage of organ donors. In vitro models of liver physiology have been developed and new technologies and approaches are progressing rapidly. Stem cells might be used as a source of liver tissue for development of models, therapies, and tissue-engineering applications. However, we have been unable to generate and maintain stable and mature adult liver cells ex vivo. We review factors that promote hepatocyte differentiation and maturation, including growth factors, transcription factors, microRNAs, small molecules, and the microenvironment. We discuss how the hepatic circulation, microbiome, and nutrition affect liver function, and the criteria for considering cells derived from stem cells to be fully mature hepatocytes. We explain the challenges to cell transplantation and consider future technologies for use in hepatic stem cell maturation, including 3-dimensional biofabrication and genome modification.