Rapid developments in stem cell research in recent years have provided a solid foundation for their use in medicine. Over the last few years, hundreds of clinical trials have been initiated in a wide panel of indications. Disorders and injuries of the nervous system still remain a challenge for the regenerative medicine. Neural stem cells (NSCs) are the optimal cells for the central nervous system restoration as they can differentiate into mature cells and, most importantly, functional neurons and glial cells. However, their application is limited by multiple factors such as difficult access to source material, limited cells number, problematic, long and expensive cultivation in vitro, and ethical considerations. On the other hand, according to the available clinical databases, most of the registered clinical trials involving cell therapies were carried out with the use of mesenchymal stem/stromal/signalling cells (MSCs) obtained from afterbirth or adult human somatic tissues. MSCs are the multipotent cells which can also differentiate into neuron-like and glia-like cells under proper conditions in vitro; however, their main therapeutic effect is more associated with secretory and supportive properties. MSCs, as a natural component of cell niche, affect the environment through immunomodulation as well as through the secretion of the trophic factors. In this review, we discuss various therapeutic strategies and activated mechanisms related to bilateral MSC–NSC interactions, differentiation of MSCs towards the neural cells (subpopulation of crest-derived cells) under the environmental conditions, bioscaffolds, or co-culture with NSCs by recreating the conditions of the neural cell niche.