Organs-on-chips (OoCs), also known as microphysiological systems or ‘tissue chips’ (the terms are synonymous), have attracted substantial interest in recent years owing to their potential to be informative at multiple stages of the drug discovery and development process. These innovative devices could provide insights into normal human organ function and disease pathophysiology, as well as more accurately predict the safety and efficacy of investigational drugs in humans. Therefore, they are likely to become useful additions to traditional preclinical cell culture methods and in vivo animal studies in the near term, and in some cases replacements for them in the longer term. In the past decade, the OoC field has seen dramatic advances in the sophistication of biology and engineering, in the demonstration of physiological relevance and in the range of applications. These advances have also revealed new challenges and opportunities, and expertise from multiple biomedical and engineering fields will be needed to fully realize the promise of OoCs for fundamental and translational applications. This Review provides a snapshot of this fast-evolving technology, discusses current applications and caveats for their implementation, and offers suggestions for directions in the next decade.