Nerve tissue damage produces a significant decrease in the quality of life and represents a considerable public health burden in the United States and in the world. Current treatment methods are mostly preventative and suggestive, and even with existing technologies, progress is limited due to the complexity of the nervous system. Nerve tissue engineering is one of the most promising methods to restore a nervous system back to good health. Astrocytes (nerve glial cells) play a pivotal role in the health of the nervous system and are fundamental for controlling several activities, from synaptic transmission to homeostasis. Astrocytes are involved in all types of brain pathologies from acute lesions to chronic neurodegenerative processes and psychiatric diseases. Effective scaffold design with polymer blending plays a crucial role in nerve tissue engineering. In this dissertation, four types of electrospun fibers were created: polycaprolactone (PCL), PCL-graphene, PCL-fullerene, and PCL-carbon nanotube (CNT) at 0.05%, 0.1%, and 0.2% by weight. From these fibers, scaffolds having nano-sized diameters were successfully fabricated. Microscopic, goniometric, thermal, x-ray, spectral, and electrical characterizations were performed to study the structural characteristics, surface free energy, crystallinity, chemical/molecular composition, and dielectric properties of these scaffolds. Toxicity levels of all scaffolds were very low. Astrocytes harvested from neonatal rats were successfully cultured on these scaffolds. An immunostaining process using rhodamine phalloidin confirmed the presence of F-actin filaments, and the anti-glial fibrillary acidic protein (GFAP) antibody test confirmed the presence of GFAP, which is a characteristic of only astrocytes. Scanning electron microscopy (SEM) analysis further confirmed the healthy morphology and successful attachment of astrocytes to the scaffolds. Apart from PCL fibers, the PCL-CNT fibers seemed to have the highest cell adhesion and proliferation.