Exposure to anesthetic drugs has been proven to seriously affect developing animals in terms of neural stem cells' (NSCs') proliferation, differentiation, and apoptosis. This can severely hamper the development of physiological learning and memory skills. Studies on the effects of anesthetics on NSCs' proliferation and differentiation are thus reviewed here, with the aim to highlight which specific drug mechanisms are the least harmful to NSCs. PubMed has been used as the preferential searching database of relevant literature to identify studies on the effects and mechanisms of NSCs' proliferation and differentiation. It was concluded that propofol and sevoflurane may be the safest options for NSCs during pregnancy and in pediatric clinical procedures, while dexmedetomidine has been found to reduce opioid-related damage in NSCs. It was also found that the growth environment may impact neurodevelopment even more than narcotic drugs. Nonetheless, the current scientific literature available further highlights how more extensive clinical trials are absolutely required for corroborating the conclusion drawn here.