Drug-induced liver injury (DILI) is a leading cause of drug attrition. Significant and well-documented differences between animals and humans in liver pathways now necessitate the use of human-relevant in vitro liver models for testing new chemical entities during preclinical drug development. Consequently, several human liver models with various levels of in vivo-like complexity have been developed for assessment of drug metabolism, toxicity, and efficacy on liver diseases. Recent trends leverage engineering tools, such as those adapted from the semiconductor industry, to enable precise control over the microenvironment of liver cells and to allow for miniaturization into formats amenable for higher throughput drug screening. Integration of liver models into organs-on-a-chip devices, permitting crosstalk between tissue types, is actively being pursued to obtain a systems-level understanding of drug effects. Here, we review the major trends, challenges, and opportunities associated with development and implementation of engineered liver models created from primary cells, cell lines, and stem cell-derived hepatocyte-like cells. We also present key applications where such models are currently making an impact and highlight areas for improvement. In the future, engineered liver models will prove useful for selecting drugs that are efficacious, safer, and, in some cases, personalized for specific patient populations