Coupled systems of in vitro microfabricated organs-on-a-chip containing small populations of human cells are being developed to address the formidable pharmacological and physiological gaps between monolayer cell cultures, animal models, and humans that severely limit the speed and efficiency of drug development. These gaps present challenges not only in tissue and microfluidic engineering, but also in systems biology: how does one model, test, and learn about the communication and control of biological systems with individual organs-on-chips that are one-thousandth or one-millionth of the size of adult organs, or even smaller, i.e., organs for a milliHuman (mHu) or microHuman (μHu)? Allometric scaling that describes inter-species variation of organ size and properties provides some guidance, but given the desire to utilize these systems to extend and validate human pharmacokinetic and pharmacodynamic (PK/PD) models in support of drug discovery and development, it is more appropriate to scale each organ functionally to ensure that it makes the suitable physiological contribution to the coupled system. The desire to recapitulate the complex organ-organ interactions that result from factors in the blood and lymph places a severe constraint on the total circulating fluid (~5 mL for a mHu and ~5 μL for a μHu) and hence on the pumps, valves, and analytical instruments required to maintain and study these systems. Scaling arguments also provide guidance on the design of a universal cell-culture medium, typically without red blood cells. This review presents several examples of scaling arguments and discusses steps that should ensure the success of this endeavour.