Delayed neurocognitive recovery and postoperative neurocognitive disorders are major complications of surgery, hospitalization, and anesthesia that are receiving increasing attention. Their incidence is reported to be 10–80% after cardiac surgery and 10–26% after non-cardiac surgery. Some of the risk factors include advanced age, level of education, history of diabetes mellitus, malnutrition, perioperative hyperglycemia, depth of anesthesia, blood pressure fluctuation during surgery, chronic respiratory diseases, etc. Scientific evidence suggests a causal association between anesthesia and delayed neurocognitive recovery or postoperative neurocognitive disorders, and various pathophysiological mechanisms have been proposed: mitochondrial dysfunction, neuroinflammation, increase in tau protein phosphorylation, accumulation of amyloid-β protein, etc. Insulin receptors in the central nervous system have a non-metabolic role and act through a neuromodulator-like action, while an interaction between anesthetics and central nervous system insulin receptors might contribute to anesthesia-induced delayed neurocognitive recovery or postoperative neurocognitive disorders. Acute or chronic intranasal insulin administration, which has no influence on the blood glucose concentration, appears to improve working memory, verbal fluency, attention, recognition of objects, etc., in animal models, cognitively healthy humans, and memory-impaired patients by restoring the insulin receptor signaling pathway, attenuating anesthesia-induced tau protein hyperphosphorylation, etc. The aim of this review is to report preclinical and clinical evidence of the implication of intranasal insulin for preventing changes in the brain molecular pattern and/or neurobehavioral impairment, which influence anesthesia-induced delayed neurocognitive recovery or postoperative neurocognitive disorders.