The vascular system is one of the first to develop during embryogenesis and is essential for all organs and tissues in our body to develop and function. It has many essential roles including controlling the absorption, distribution and excretion of compounds and therefore determines the pharmacokinetics of drugs and therapeutics. Vascular homeostasis is under tight physiological control which is essential for maintaining tissues in a healthy state. Consequently, disruption of vascular homeostasis plays an integral role in many disease processes, making cells of the vessel wall attractive targets for therapeutic intervention. Experimental models of blood vessels can therefore contribute significantly to drug development and aid in predicting the biological effects of new drug entities. The increasing availability of human induced pluripotent stem cells (hiPSC) derived from healthy individuals and patients have accelerated advances in developing experimental in vitro models of the vasculature: human endothelial cells (ECs), pericytes and vascular smooth muscle cells (VSMCs), can now be generated with high efficiency from hiPSC and used in 'microfluidic chips' (also known as 'organ-on-chip' technology) as a basis for in vitro models of blood vessels. These near physiological scaffolds allow the controlled integration of fluid flow and three-dimensional (3D) co-cultures with perivascular cells to mimic tissue- or organ-level physiology and dysfunction in vitro. Here, we review recent multidisciplinary developments in these advanced experimental models of blood vessels that combine hiPSC with microfluidic organ-on-chip technology. We provide examples of their utility in various research areas and discuss steps necessary for further integration in biomedical applications so that they can be contribute effectively to the evaluation and development of new drugs and other therapeutics as well as personalized (patient-specific) treatments.