The number of elderly patients who frequently access health care services is increasing worldwide. While anesthesiologists are developing the expertise to care for these elderly patients, areas of concern remain. We conducted a comprehensive search of major international databases (PubMed, Embase, and Cochrane) and a Korean database (KoreaMed) to review preoperative considerations, intraoperative management, and postoperative problems when anesthetizing elderly patients. Preoperative preparation of elderly patients included functional assessment to identify preexisting cognitive impairment or cardiopulmonary reserve, depression, frailty, nutrition, polypharmacy, and anticoagulation issues. Intraoperative management included anesthetic mode and pharmacology, monitoring, intravenous fluid or transfusion management, lung-protective ventilation, and prevention of hypothermia. Postoperative checklists included perioperative analgesia, postoperative delirium and cognitive dysfunction, and other complications. A higher level of perioperative care was required for older surgical patients, as multiple chronic diseases often makes them prone to developing postoperative complications, including functional decline and loss of independence. Although the guiding evidence remains poor so far, elderly patients have to be provided optimal perioperative care through close interdisciplinary, interprofessional, and cross-sectional collaboration to minimize unwanted postoperative outcomes. Furthermore, along with adequate anesthetic care, well-planned postoperative care should begin immediately after surgery and extend until discharge.