In recent years, the need for sophisticated human in vitro models for integrative biology has motivated the development of organ-on-a-chip platforms. Organ-on-a-chip devices are engineered to mimic the mechanical, biochemical and physiological properties of human organs; however, there are many important considerations when selecting or designing an appropriate device for investigating a specific scientific question. Building microfluidic Brain-on-a-Chip (BoC) models from the ground-up will allow for research questions to be answered more thoroughly in the brain research field, but the design of these devices requires several choices to be made throughout the design development phase. These considerations include the cell types, extracellular matrix (ECM) material(s), and perfusion/flow considerations. Choices made early in the design cycle will dictate the limitations of the device and influence the end-point results such as the permeability of the endothelial cell monolayer, and the expression of cell type-specific markers. To better understand why the engineering aspects of a microfluidic BoC need to be influenced by the desired biological environment, recent progress in microfluidic BoC technology is compared. This review focuses on perfusable blood–brain barrier (BBB) and neurovascular unit (NVU) models with discussions about the chip architecture, the ECM used, and how they relate to the in vivo human brain. With increased knowledge on how to make informed choices when selecting or designing BoC models, the scientific community will benefit from shorter development phases and platforms curated for their application.