In vitro models of biological tissues are indispensable tools for unraveling human physiology and pathogenesis. They usually consist of a single layer of a single cell type, which makes them robust and suitable for parallelized research. However, due to their simplicity, in vitro models are also less valid as true reflections of the complex biological tissues of the human body. Even though the realism of the models can be increased by including more cell types, this will inevitably lead to a decrease in robustness and throughput. The constant trade-off between realism and simplicity has led to an impasse in the development of new in vitro models. Organs-on-chips, a class of microengineered in vitro tissue models, have the potential to break the in vitro impasse. These models combine an artificially engineered, physiologically realistic cell culture microenvironment with the potential for parallelization and increased throughput. They are robust, because the engineered physiological, organ-level features such as tissue organization, geometry, soluble gradients and mechanical stimulation are well-defined and controlled. Moreover, their microfluidic properties and integrated sensors pave the way for high-throughput studies. In this review, we define the in vitro impasse, we explain why organs-on-chips have the potential to break the impasse and we formulate a view on the future of the field. We focus on the design philosophy of organs-on-chips, the integration of technology and biology and on how to connect to the potential end-users.