With the accelerating pace of brain research in recent years and the growing appreciation of the complexity of the brain and several brain-associated neurological diseases, the demand for powerful tools to enhance drug screening, diagnosis, and fundamental research is greater than ever. Highly representative models of the central nervous system (CNS) can play a critical role in meeting these needs. Unfortunately, in vivo animal models lack controllability, are difficult to monitor, and do not model human-specific brain behavior accurately. On the other hand, in silico computational models struggle to capture comprehensively the intertwined biological, chemical, electrical, and mechanical complexity of the brain. This leaves us with the promising domain of "organ-on-chip" in vitro models. In this review, we describe some of the most pioneering efforts in this expanding field, offering a perspective on the new possibilities as well as the limitations of each approach. We focus particularly on how the models reproduce the blood-brain barrier (BBB), which mediates mass transport to and from brain tissue. We also offer a brief commentary on strategies for evaluating the blood-brain barrier functionality of these in vitro models, including trans-endothelial electrical resistance (TEER), immunocytochemistry, and permeability analysis. From the early membrane-based models of the BBB that have grown into the Transwell® class of devices, to the era of microfluidic chips and a future of bio-printed tissue, we see enormous improvement in the reliability of in vitro models. More and more of the biological and structural complexity of the BBB is being captured by microfluidic chips, and the organ-specificity of bio-printed tissue is also significantly improved. Although we believe that the long-term solution will eventually take the form of automated and parallelized bio-printing systems, we find that valuable transport studies can already be accomplished with microfluidic platforms.