Microphysiological systems (MPSs) are cellular models that replicate aspects of organ and tissue functions in vitro. In contrast with conventional cell cultures, MPSs often provide physiological mechanical cues to cells, include fluid flow and can be interlinked (hence, they are often referred to as microfluidic tissue chips or organs-on-chips). Here, by means of examples of MPSs of the vascular system, intestine, brain and heart, we advocate for the development of standards that allow for comparisons of quantitative physiological features in MPSs and humans. Such standards should ensure that the in vivo relevance and predictive value of MPSs can be properly assessed as fit-for-purpose in specific applications, such as the assessment of drug toxicity, the identification of therapeutics or the understanding of human physiology or disease. Specifically, we distinguish designed features, which can be controlled via the design of the MPS, from emergent features, which describe cellular function, and propose methods for improving MPSs with readouts and sensors for the quantitative monitoring of complex physiology towards enabling wider end-user adoption and regulatory acceptance.