The neurovascular unit (NVU), consisting of neurons, glial cells, vascular cells (endothelial cells, pericytes and vascular smooth muscle cells (VSMCs)) together with the surrounding extracellular matrix (ECM), is an important interface between the peripheral blood and the brain parenchyma. Disruption of the NVU impacts on blood–brain barrier (BBB) regulation and underlies the development and pathology of multiple neurological disorders, including stroke and Alzheimer’s disease (AD). The ability to differentiate induced pluripotent stem cells (iPSCs) into the different cell types of the NVU and incorporate them into physical models provides a reverse engineering approach to generate human NVU models to study BBB function. To recapitulate the in vivo situation such NVU models must also incorporate the ECM to provide a 3D environment with appropriate mechanical and biochemical cues for the cells of the NVU. In this review, we provide an overview of the cells of the NVU and the surrounding ECM, before discussing the characteristics (stiffness, functionality and porosity) required of hydrogels to mimic the ECM when incorporated into in vitro NVU models. We summarise the approaches available to measure BBB functionality and present the techniques in use to develop robust and translatable models of the NVU, including transwell models, hydrogel models, 3D-bioprinting, microfluidic models and organoids. The incorporation of iPSCs either without or with disease-specific genetic mutations into these NVU models provides a platform in which to study normal and disease mechanisms, test BBB permeability to drugs, screen for new therapeutic targets and drugs or to design cell-based therapies.