Understanding the cellular basis of neurological disorders have advanced at a slow pace, especially due to the extreme invasiveness of brain biopsying and limitations of cell lines and animal models that have been used. Since the derivation of pluripotent stem cells (PSCs), a novel source of cells for regenerative medicine and disease modeling has become available, holding great potential for the neurology field. However, safety for therapy and accurateness for modeling have been a matter of intense debate, considering that genomic instability, including the gain and loss of chromosomes (aneuploidy), has been repeatedly observed in those cells. Despite the fact that recent reports have described some degree of aneuploidy as being normal during neuronal differentiation and present in healthy human brains, this phenomenon is particularly controversial since it has traditionally been associated with cancer and disabling syndromes. It is therefore necessary to appreciate, to which extent, aneuploid pluripotent stem cells are suitable for regenerative medicine and neurological modeling and also the limits that separate constitutive from disease-related aneuploidy. In this review, recent findings regarding chromosomal instability in PSCs and within the brain will be discussed.