Durum wheat is one of the most commonly cultivated species in the world and represents a key commodity for many areas worldwide, as its grain is used for production of many foods, such as pasta, bread, couscous, and bourghul. Durum wheat grain has a relevant role in the human diet, providing carbohydrates, proteins, lipids, fibres, vitamins, and minerals, as well as highly valued bioactive compounds contributing to a healthy diet. Durum wheat is largely cultivated in the Mediterranean basin, where it is mainly grown under rain-fed conditions, thus currently undergoing drought stress, as well as soil salinity, which can hamper yield potential and influence the qualitative characteristics of grain. When plants suffer drought and/or salinity stress, a condition known as hyperosmotic stress is established at cellular level. This leads to the accumulation of ROS thus generating in turn an oxidative stress condition, which can ultimately result in the impairment of cellular integrity and functionality. To counteract oxidative damage due to excessive ROS production under stress, plants have evolved a complex array of both enzymatic and non-enzymatic antioxidant mechanisms, working jointly and synergically for maintenance of ROS homeostasis. Enhancement of antioxidant defence system has been demonstrated as an adaptive mechanism associated to an increased tolerance to hyperosmotic stress. In the light of these considerations, this review provides a concise overview on recent advancements regarding the role of the ascorbate-glutathione cycle and the main antioxidant enzymes (superoxide dismutase, catalase, and peroxidases) in durum wheat response to drought and salt stresses that are expected to become more and more frequent due to the ongoing climate changes.