Potato (Solanum tuberosum L.), as a shallow-rooted crop, is relatively sensitive to soil water deficits; therefore, irrigation plays a crucial role in achieving economically viable production and quality. However, due to the scarcity of water, which has become more precious and less available due to climate change, it is essential to optimize irrigation management and enhance water productivity. The present systematic review, drawing on the most relevant scientific literature, discusses the current state of knowledge on irrigation management and water productivity in potato crop production in semi-arid regions, particularly within Mediterranean countries. Overall, the main findings indicate different possible solutions for saving irrigation water and increasing water productivity by adopting a combination of water-saving strategies, such as static or dynamic deficit irrigation, or partial root-zone drying, and by using a suitable irrigation method like drip irrigation. In addition, the importance of other agronomic factors, namely planting dates, soil texture, and fertilization management, has also emerged, prompting scientists to pay greater attention to them in the future, along with the selection or breeding of appropriate cultivars, which may represent the long-term solution to the problem of water scarcity.