The design of neural tissue models with architectural and biochemical relevance to native tissues opens the way for the fundamental study and development of therapies for many disorders with limited treatment options. Here, we systematically review the most recent literature on 3D bioprinted neural models, including their potential for use in drug screening. Neural tissues that model the central nervous system (CNS) from the relevant literature are reviewed with comprehensive summaries of each study, and discussion of the model types, bioinks and additives, cell types used, bioprinted construct shapes and culture time, and the characterization methods used. In this review, we accentuate the lack of standardization among characterization methods to analyze the functionality (including chemical, metabolic and other pathways) and mechanical relevance of the 3D bioprinted constructs, and discuss this as a critical area for future exploration. These gaps must be addressed for this technology to be applied for effective drug screening applications, despite its enormous potential for rapid and efficient drug screening. The future of biomimetic, 3D printed neural tissues is promising and evaluation of the in vivo relevance on multiple levels should be sought to adequately compare model performance and develop viable treatment options for neurodegenerative diseases, or other conditions that affect the CNS.