Understanding the physiopathology of disease remains an essential step in developing novel therapeutics. Although animal models have certainly contributed to advancing this enterprise, their limitation in modeling all the aspects of complex human disorders is one of the major challenges faced by the biomedical research field. Human induced pluripotent stem cells (hiPSCs) derived from patients represent a great opportunity to overcome this deficiency because these cells cover the genetic diversity needed to fully model human diseases. Here, we provide an overview of the history of hiPSC technology and discuss common challenges and approaches that we and others have faced when using hiPSCs to model disease. Our emphasis is on liver disease, and consequently, we review the progress made using this technology to produce functional liver cells in vitro and how these systems are being used to recapitulate a diversity of developmental, metabolic, genetic, and infectious liver disorders.