Anesthesia in older patients is challenging and requires a range of skills in various techniques, both during surgery and in the post-operative period. Post-operative delirium is one of the most common cognitive dysfunctions after surgery, and elderly patients are at the highest risk. The pathophysiology of post-operative delirium remains incompletely understood. Several mechanisms (vascular, neurodegenerative, neuroimmune, neuroinflammation, drug-induced, stress-induced, and monoaminergic) have been considered to play a role. The type of anesthesia—general (gas, total intravenous), regional, or combined—was identified as a predictive factor. However, numerous prospective and retrospective studies have failed to determine which anesthetic technique is the best for preventing post-operative delirium. The type of surgery appears to be more critical than the type of anesthesia. However, the development of post-operative cognitive dysfunction could be linked to the depth of anesthesia. Dexmedetomidine displayed promising therapeutic potential for the efficient prevention or treatment of hyperactive post-operative delirium. The management of hypoactive post-operative delirium still requires further investigations, particularly in elderly patients.