Most common drug development failures originate from either bioavailability problems, or unexpected toxic effects. The culprit is often the liver, which is responsible for biotransformation of a majority of xenobiotics. Liver may be modeled using "liver on a chip" devices, which may include established cell lines, primary human cells, and stem cell-derived hepatocyte-like cells. The choice of biological material along with its processing and maintenance greatly influence both the device performance and the resultant toxicity predictions. Impediments to the development of "liver on a chip" technology include the problems with standardization of cells, limitations imposed by culturing and the necessity to develop more complicated fluidic contours. Fortunately, recent breakthroughs in the development of cell-based reporters, including ones with fluorescent label, permits monitoring of the behavior of the cells embed into the "liver on a chip" devices. Finally, a set of computational approaches has been developed to model both particular toxic response and the homeostasis of human liver as a whole; these approaches pave a way to enhance the in silico stage of assessment for a potential toxicity.