Physiologically relevant and broadly applicable liver cell culture platforms are of great importance in both drug development and disease modeling. Organ-on-a-chip systems offer a promising alternative to conventional, static two-dimensional (2-D) cultures, providing much-needed cues such as perfusion, shear stress, and three-dimensional (3-D) cell-cell communication. However, such devices cover a broad range of complexity both in manufacture and in implementation. In this review, we summarize the key features of the human liver that should be reflected in a physiologically relevant liver-on-a-chip model. We also discuss different material properties of importance in producing liver-on-a-chip devices and summarize recent and current progress in the field, highlighting different types of devices at different levels of complexity.