Plants are often exposed to unfavorable environmental conditions, for instance abiotic stresses, which dramatically alter distribution of plant species among ecological niches and limit the yields of crop species. Among these, drought stress is one of the most impacting factors which alter seriously the plant physiology, finally leading to the decline of the crop productivity. Drought stress causes in plants a set of morpho-anatomical, physiological and biochemical changes, mainly addressed to limit the loss of water by transpiration with the attempt to increase the plant water use efficiency. The stomata closure, one of the first consistent reactions observed under drought, results in a series of consequent physiological/biochemical adjustments aimed at balancing the photosynthetic process as well as at enhancing the plant defense barriers against drought-promoted stress (e.g., stimulation of antioxidant systems, accumulation of osmolytes and stimulation of aquaporin synthesis), all representing an attempt by the plant to overcome the unfavorable period of limited water availability. In view of the severe changes in water availability imposed by climate change factors and considering the increasing human population, it is therefore of outmost importance to highlight: (i) how plants react to drought; (ii) the mechanisms of tolerance exhibited by some species/cultivars; and (iii) the techniques aimed at increasing the tolerance of crop species against limited water availability. All these aspects are necessary to respond to the continuously increasing demand for food, which unfortunately parallels the loss of arable land due to changes in rainfall dynamics and prolonged period of drought provoked by climate change factors. This review summarizes the most updated findings on the impact of drought stress on plant morphological, biochemical and physiological features and highlights plant mechanisms of tolerance which could be exploited to increase the plant capability to survive under limited water availability. In addition, possible applicative strategies to help the plant in counteracting unfavorable drought periods are also discussed.