Lesion or disease of the somatosensory system leads to the development of neuropathic pain. Peripheral neuropathic pain encompasses damage or injury of the peripheral nervous system. On the other hand, 10–15% of individuals suffer from acute postoperative pain followed by persistent pain after undergoing surgeries. Antidepressants, anticonvulsants, baclofen, and clonidine are used to treat peripheral neuropathy, whereas opioids are used to treat postoperative pain. The negative effects associated with these drugs emphasize the search for alternative therapeutics with better efficacy and fewer side effects. Curcumin, a polyphenol isolated from the roots of Curcuma longa, possesses antibacterial, antioxidant, and anti-inflammatory properties. Furthermore, the low bioavailability and fast metabolism of curcumin have led to the advent of various curcumin formulations. The present review provides a comprehensive analysis on the effects of curcumin and its formulations in preclinical and clinical studies of neuropathic and postoperative pain. Based on the positive outcomes from both preclinical and clinical studies, curcumin holds the promise of mitigating or preventing neuropathic and postoperative pain conditions. However, more clinical studies with improved curcumin formulations are required to involve its use as adjuvant to neuropathic and postoperative drugs.