Aging is associated with widespread structural and functional changes in the brain including reduced neural plasticity, slower information processing, and impaired network integration. These age-related alterations influence the brain’s response to anesthetic agents, particularly electroencephalography (EEG) activity. This narrative review summarizes the characteristic EEG features induced by commonly used hypnotic agents such as propofol, inhaled anesthetics, dexmedetomidine, ketamine, and remimazolam in elderly patients and examines how aging modulates these responses. With increasing age, EEG power shows a global decline, most prominently in the alpha frequency band (8–13 Hz), reflecting reduced thalamocortical and cortical activity. Peak alpha frequency slows progressively with age, and background EEG also often exhibits characteristic slowing, both of which are associated with cognitive decline. In addition, EEG reactivity to external stimuli diminishes, and integrative brain activity, representing coordinated processing across cortical regions, is reduced in older adults. Frontoparietal feedback connectivity, essential for conscious perception and information integration, is particularly weak in the elderly. These changes are further exacerbated under anesthesia, as general anesthetics disrupt top-down connectivity and reduce network integration. Graph-theoretical EEG analyses reveal age-related reductions in global efficiency, modularity, and small-world properties, which are signatures of a less efficient, more random, and fragmented brain network. Understanding these age-specific EEG alterations can improve intraoperative monitoring, anesthetic titration, and development of age-tailored EEG-guided strategies. Future research should aim to validate EEG biomarkers that reliably reflect anesthetic depth and brain health in elderly populations, thereby fostering safer anesthesia care in the aging population.