Tissue engineering strategies employing biomaterials have made great progress in the last few decades. However, the tissues of the brain and spinal cord pose unique challenges due to a separate immune system and their nature as soft tissue. Because of this, neural tissue engineering for the brain and spinal cord may require re-establishing biocompatibility and functionality of biomaterials that have previously been successful for tissue engineering in the body. The goal of this review is to briefly describe the distinctive properties of the central nervous system, specifically the neuroimmune response, and to describe the factors which contribute to building polymer hydrogels compatible with this tissue. These factors include polymer chemistry, polymerization and degradation, and the physical and mechanical properties of the hydrogel. By understanding the necessities in making hydrogels biocompatible with tissue of the brain and spinal cord, tissue engineers can then functionalize these materials for repairing and replacing tissue in the central nervous system.