Translational challenges associated with reductionist modeling approaches, as well as ethical concerns and economic implications associated with small animal testing, drive the need for developing microphysiological neural systems for modeling human neurological diseases, disorders and injuries. Here, we provide a comprehensive review of microphysiological neural systems on a chip (NSCs) for modeling higher order trajectories in the human nervous system. Societal, economic, and national security impacts of neurological diseases, disorders and injuries are highlighted to identify critical NSC application spaces. Hierarchical design and manufacturing of NSCs are discussed with distinction of surface- and bulk-based systems. Three broad NSC classes are identified and reviewed: microfluidic NSCs, compartmentalized NSCs, and hydrogel NSCs. Emerging areas and future directions are highlighted, including the application of 3D printing to design and manufacturing of next-generation NSCs, the use of stem cells for constructing patient-specific NSCs, and the application of human NSCs to ‘personalized neurology’. Technical hurdles and remaining challenges are discussed. This review identifies the state-of-the-art design methodologies, manufacturing approaches, and performance capabilities of NSCs. This work suggests NSCs appear poised to revolutionize the modeling of human neurological diseases, disorders and injuries.