“Mice are not little people” – a refrain becoming louder as the gaps between animal models and human disease become more apparent. At the same time, three emerging approaches are headed toward integration: powerful systems biology analysis of cell-cell and intracellular signaling networks in patient-derived samples; 3D tissue engineered models of human organ systems, often made from stem cells; and micro-fluidic and meso-fluidic devices that enable living systems to be sustained, perturbed and analyzed for weeks in culture. Integration of these rapidly moving fields has the potential to revolutionize development of therapeutics for complex, chronic diseases, including those that have weak genetic bases and substantial contributions from gene-environment interactions. Technical challenges in modeling complex diseases with “organs on chips” approaches include the need for relatively large tissue masses and organ-organ cross talk to capture systemic effects, such that current microfluidic formats often fail to capture the required scale and complexity for interconnected systems. These constraints drive development of new strategies for designing in vitro models, including perfusing organ models, as well as “mesofluidic” pumping and circulation in platforms connecting several organ systems, to achieve the appropriate physiological relevance.