For centuries, animal experiments have contributed much to our understanding of mechanisms of human disease, but their value in predicting the effectiveness of drug treatments in the clinic has remained controversial. Animal models, including genetically modified ones and experimentally induced pathologies, often do not accurately reflect disease in humans, and therefore do not predict with sufficient certainty what will happen in humans. Organ-on-chip (OOC) technology and bioengineered tissues have emerged as promising alternatives to traditional animal testing for a wide range of applications in biological defence, drug discovery and development, and precision medicine, offering a potential alternative. Recent technological breakthroughs in stem cell and organoid biology, OOC technology, and 3D bioprinting have all contributed to a tremendous progress in our ability to design, assemble and manufacture living organ biomimetic systems that more accurately reflect the structural and functional characteristics of human tissue in vitro, and enable improved predictions of human responses to drugs and environmental stimuli. Here, we provide a historical perspective on the evolution of the field of bioengineering, focusing on the most salient milestones that enabled control of internal and external cell microenvironment. We introduce the concepts of OOCs and Microphysiological systems (MPSs), review various chip designs and microfabrication methods used to construct OOCs, focusing on blood-brain barrier as an example, and discuss existing challenges and limitations. Finally, we provide an overview on emerging strategies for 3D bioprinting of MPSs and comment on the potential role of these devices in precision medicine.