In recent years, advances in tissue engineering and microfabrication technologies have enabled rapid growth in the areas of in vitro organoid development as well as organoid-on-a-chip platforms. These 3D model systems often are able to mimic human physiology more accurately than traditional 2D cultures and animal models. In this review, we describe the progress that has been made to generate organ-on-a-chip platforms and, more recently, more complex multi-organoid body-on-a-chip platforms and their applications. Importantly, these systems have the potential to dramatically impact biomedical applications in the areas of drug development, drug and toxicology screening, disease modeling, and the emerging area of personalized precision medicine.