Anesthesia and surgery are delivered to a temporally organized organism whose physiology is governed by the suprachiasmatic nucleus, peripheral molecular clocks, and pineal melatonin signaling. This review synthesizes mechanistic, preclinical, and clinical evidence on how anesthetic agents, surgical stress, and the perioperative environment interact with circadian and melatonergic signaling, and on whether that interaction can be targeted therapeutically. In rodent and cellular studies, volatile and intravenous anesthetics alter clock function in an agent- and phase-dependent manner; proposed mechanisms include GABAergic and glutamatergic modulation of entrainment, transcriptional and chromatin-level repression of CLOCK-BMAL1/PER-CRY signaling, and metabolic coupling through CaMK-CREB, AMPK, SIRT1, and GSK-3β. These mechanisms have not been confirmed in humans. In patients, these effects are inseparable from surgical injury, opioids, fasting, inflammation, and disrupted light-dark exposure, all of which suppress melatonin amplitude, delay its onset, and promote internal desynchrony. Melatonin signals through MT1 and MT2 receptors to produce chronobiotic, anxiolytic, and antinociceptive effects, whereas the mitochondrial, redox, and anti-inflammatory actions, described almost exclusively in animal and cellular models, require substantially higher exposures and have not been demonstrated in surgical patients; the two arms are pharmacologically distinct and should not be pooled. Clinically, preoperative anxiolysis with melatonin in adults is the most consistently supported indication, whereas evidence for postoperative sleep, analgesia, delirium prevention, and organ protection remains heterogeneous and of low certainty. Most trials have used fixed clock-time dosing without measuring internal circadian phase or achieved plasma exposure, so null results cannot distinguish an ineffective mechanism from an inadequate intervention. The circadian-melatonin axis remains a plausible perioperative target, but clinical translation requires phase-aware, exposure-informed, and adequately powered trials.