Neurological disorders are the leading cause of disability and the second largest cause of death worldwide. Despite significant research efforts, neurology remains one of the most failure-prone areas of drug development. The complexity of the human brain, boundaries to examining the brain directly in vivo, and the significant evolutionary gap between animal models and humans, all serve to hamper translational success. Recent advances in microfluidic in vitro models have provided new opportunities to study human cells with enhanced physiological relevance. The ability to precisely micro-engineer cell-scale architecture, tailoring form and function, has allowed for detailed dissection of cell biology using microphysiological systems (MPS) of varying complexities from single cell systems to "Organ-on-chip" models. Simplified neuronal networks have allowed for unique insights into neuronal transport and neurogenesis, while more complex 3D heterotypic cellular models such as neurovascular unit mimetics and "Organ-on-chip" systems have enabled new understanding of metabolic coupling and blood-brain barrier transport. These systems are now being developed beyond MPS toward disease specific micro-pathophysiological systems, moving from "Organ-on-chip" to "Disease-on-chip." This review gives an outline of current state of the art in microfluidic technologies for neurological disease research, discussing the challenges and limitations while highlighting the benefits and potential of integrating technologies. We provide examples of where such toolsets have enabled novel insights and how these technologies may empower future investigation into neurological diseases.