Over many decades, constructing genetically and phenotypically stable lines of neural stem cells (NSC) for clinical purposes with the aim of restoring irreversibly lost functions of nervous tissue has been one of the major goals for multiple research groups. The unique ability of stem cells to maintain their own pluripotent state even in the adult body has made them into the choice object of study. With the development of the technology for induced pluripotent stem cells (iPSCs) and direct transdifferentiation of somatic cells into the desired cell type, the initial research approaches based on the use of allogeneic NSCs from embryonic or fetal nervous tissue are gradually becoming a thing of the past. This review deals with basic molecular mechanisms for maintaining the pluripotent state of embryonic/induced stem and reprogrammed somatic cells, as well as with currently existing reprogramming strategies. The focus is on performing direct reprogramming while bypassing the stage of iPSCs which is known for genetic instability and an increased risk of tumorigenesis. A detailed description of various protocols for obtaining reprogrammed neural cells used in the therapy of the nervous system pathology is also provided.