Conductive biomaterials provide an important control for engineering neural tissues, where electrical stimulation can potentially direct neural stem/progenitor cell (NS/PC) maturation into functional neuronal networks. It is anticipated that stem cell-based therapies to repair damaged central nervous system (CNS) tissues and ex vivo, "tissue chip" models of the CNS and its pathologies will each benefit from the development of biocompatible, biodegradable, and conductive biomaterials. Here, technological advances in conductive biomaterials are reviewed over the past two decades that may facilitate the development of engineered tissues with integrated physiological and electrical functionalities. First, one briefly introduces NS/PCs of the CNS. Then, the significance of incorporating microenvironmental cues, to which NS/PCs are naturally programmed to respond, into biomaterial scaffolds is discussed with a focus on electrical cues. Next, practical design considerations for conductive biomaterials are discussed followed by a review of studies evaluating how conductive biomaterials can be engineered to control NS/PC behavior by mimicking specific functionalities in the CNS microenvironment. Finally, steps researchers can take to move NS/PC-interfacing, conductive materials closer to clinical translation are discussed.