The incidence of nerve tissue injuries, such as peripheral nerve injury, spinal cord injury, traumatic brain injury, and various neurodegenerative diseases (NDs), is continuously increasing because of stress, physical and chemical trauma, and the aging population worldwide. Restoration of the damaged nervous system is challenging because of its structural and functional complexity and limited regenerative ability. Additionally, there is no cure available for NDs except for medications that provide symptomatic relief. Stem cells offer an alternative approach for promoting damage repair, but their efficacy is limited by a compromised survival rate and neurogenesis process. To address these challenges, neural tissue engineering has emerged as a promising strategy in which stem cells are seeded or encapsulated within a suitable biomaterial construct, increasing cell survival and neurogenesis. Numerous biomaterials are utilized to create different types of constructs for this purpose. Researchers are trying to develop ideal scaffolds that combine biomaterials, cells, and molecules that exactly mimic the biological and mechanical properties of the tissue to achieve functional recovery associated with neurological dysfunction. This review focuses on exploring the development and applications of different biomaterials for their potential use in the diagnosis, therapy, nerve tissue regeneration, and treatment of neurological disorders.