Ongoing clinical trials are evaluating the use of stem cells as a way to treat traumatic spinal cord injury (SCI). However, the inhibitory environment present in the injured spinal cord makes it challenging to achieve the survival of these cells along with desired differentiation into the appropriate phenotypes necessary to regain function. Transplanting stem cells along with an instructive biomaterial scaffold can increase cell survival and improve differentiation efficiency. This study reviews the literature discussing different types of instructive biomaterial scaffolds developed for transplanting stem cells into the injured spinal cord. We have chosen to focus specifically on biomaterial scaffolds that direct the differentiation of neural stem cells and pluripotent stem cells since they offer the most promise for producing the cell phenotypes that could restore function after SCI. In terms of biomaterial scaffolds, this article reviews the literature associated with using hydrogels made from natural biomaterials and electrospun scaffolds for differentiating stem cells into neural phenotypes. It then presents new data showing how these different types of scaffolds can be combined for neural tissue engineering applications and provides directions for future studies.