Oxidative stress and mitochondrial dysfunction are associated with the pathogenesis of several human diseases. The excessive generation of reactive oxygen species (ROS) and/or lack of adequate antioxidant defenses causes DNA mutations in mitochondria, damages the mitochondrial respiratory chain, and alters membrane permeability and mitochondrial defense mechanisms. All these alterations are linked to the development of numerous diseases. Curcumin, an active ingredient of turmeric plant rhizomes, exhibits numerous biological activities (i.e., antioxidant, anti-inflammatory, anticancer, and antimicrobial). In recent years, many researchers have shown evidence that curcumin has the ability to reduce the oxidative stress- and mitochondrial dysfunction-associated diseases. In this review, we discuss curcumin’s antioxidant mechanism and significance in oxidative stress reduction and suppression of mitochondrial dysfunction in mammals. We also discuss the research gaps and give our opinion on how curcumin research in mammals should proceed moving forward.