The human α7 neuronal nicotinic acetylcholine receptor gene (CHRNA7) is widely expressed in the central and peripheral nervous systems. This receptor is implicated in both brain development and adult neurogenesis thanks to its ability to mediate acetylcholine stimulus (Ach). Copy number variations (CNVs) of CHRNA7 gene have been identified in humans and are genetically linked to cognitive impairments associated with multiple disorders, including schizophrenia, bipolar disorder, epilepsy, Alzheimer’s disease, and others. Currently, α7 receptor analysis has been commonly performed in animal models due to the impossibility of direct investigation of the living human brain. But the use of model systems has shown that there are very large differences between humans and mice when researchers must study the CNVs and, in particular, the CNV of chromosome 15q13.3 where the CHRNA7 gene is present. In fact, human beings present genomic alterations as well as the presence of genes of recent origin that are not present in other model systems as well as they show a very heterogeneous symptomatology that is associated with both their genetic background and the environment where they live. To date, the induced pluripotent stem cells, obtained from patients carrying CNV in CHRNA7 gene, are a good in vitro model for studying the association of the α7 receptor to human diseases. In this review, we will outline the current state of hiPSCs technology applications in neurological diseases caused by CNVs in CHRNA7 gene. Furthermore, we will discuss some weaknesses that emerge from the overall analysis of the published articles.