The failure of animal models to predict therapeutic responses in humans is a major problem that also brings into question their use for basic research. Organ-on-a-chip (organ chip) microfluidic devices lined with living cells cultured under fluid flow can recapitulate organ-level physiology and pathophysiology with high fidelity. Here, I review how single and multiple human organ chip systems have been used to model complex diseases and rare genetic disorders, to study host–microbiome interactions, to recapitulate whole-body inter-organ physiology and to reproduce human clinical responses to drugs, radiation, toxins and infectious pathogens. I also address the challenges that must be overcome for organ chips to be accepted by the pharmaceutical industry and regulatory agencies, as well as discuss recent advances in the field. It is evident that the use of human organ chips instead of animal models for drug development and as living avatars for personalized medicine is ever closer to realization.