Unlike other tissue types, the nervous tissue extends to a wide and complex environment that provides a plurality of different biochemical and topological stimuli which in turn define the functions of that tissue. As a consequence of such complexity, the traditional transplantation therapeutic methods are quite ineffective; therefore, the restoration of peripheral and central nervous system injuries has been a continuous challenge. Tissue engineering and regenerative medicine in the nervous system have provided new alternative medical approaches. These methods use external biomaterial supports, known as scaffolds, in order to create platforms for the cells to migrate to the injury site and repair the tissue. The challenge in neural tissue engineering (NTE) remains the fabrication of scaffolds with precisely controlled, tunable topography, biochemical cues and surface energy, capable of directing and controlling the function of neuronal cells. At the same time, it has been shown that neural tissue engineering provides the potential to model neurological diseases in vitro, mainly via lab-on-a-chip systems, especially in cases for which it is difficult to obtain suitable animal models. As a consequence of the intense research activity in the field, a variety of synthetic approaches and 3D fabrication methods have been developed for the fabrication of NTE scaffolds, including soft lithography and self-assembly, as well as subtractive (top-down) and additive (bottom-up) manufacturing. This article aims at reviewing the existing research effort in the rapidly growing field related to the development of biomaterial scaffolds and lab-on-a-chip systems for NTE applications. Besides presenting recent advances achieved by NTE strategies, this work also delineates existing limitations and highlights emerging possibilities and future prospects in this field.