Viruses that infect the central nervous system (CNS) are associated with developmental abnormalities as well as neuropsychiatric and degenerative conditions. Many of these viruses such as Zika virus (ZIKV), cytomegalovirus (CMV), and herpes simplex virus (HSV) demonstrate tropism for neural stem cells (NSCs). NSCs are the multipotent progenitor cells of the brain that have the ability to form neurons, astrocytes, and oligodendrocytes. Viral infections often alter the function of NSCs, with profound impacts on the growth and repair of the brain. There are a wide spectrum of effects on NSCs, which differ by the type of virus, the model system, the cell types studied, and the age of the host. Thus, it is a challenge to predict and define the consequences of interactions between viruses and NSCs. The purpose of this review is to dissect the mechanisms by which viruses can affect survival, proliferation, and differentiation of NSCs. This review also sheds light on the contribution of key antiviral cytokines in the impairment of NSC activity during a viral infection, revealing a complex interplay between NSCs, viruses, and the immune system.