Human disease and regenerative medicine models, including formats referred to as “organ-on-chip” (OoC), are increasingly regarded as powerful tools for drug discovery, safety pharmacology and efficacy testing, in both personalized and precision medicine. Developed over the past 10 years, they constitute an important new approach to medicine and towards the replacement of animal models. To date, however, OoC models lack the lymphatic and immune system, despite their essential role in health and disease.