Neurological disorders are recognized as major causes of death and disability worldwide. Because of this, they represent one of the largest public health challenges. With awareness of the massive burden associated with these disorders, came the recognition that treatment options were disproportionately scarce and, oftentimes, ineffective. To address these problems, modern research is increasingly looking into novel, more effective methods to treat neurological patients; one of which is cell-based therapies. In this review, we present a critical analysis of the features, challenges, and prospects of one of the stem cell types that can be employed to treat numerous neurological disorders—mesenchymal stem cells (MSCs). Despite the fact that several studies have already established the safety of MSC-based treatment approaches, there are still some reservations within the field regarding their immunocompatibility, heterogeneity, stemness stability, and a range of adverse effects—one of which is their tumor-promoting ability. We additionally examine MSCs’ mechanisms of action with respect to in vitro and in vivo research as well as detail the findings of past and ongoing clinical trials for Parkinson’s and Alzheimer’s disease, ischemic stroke, glioblastoma multiforme, and multiple sclerosis. Finally, this review discusses prospects for MSC-based therapeutics in the form of biomaterials, as well as the use of electromagnetic fields to enhance MSCs’ proliferation and differentiation into neuronal cells.