Intensive irrigation and nutrient management practices in agriculture have given rise to serious issues in aquifer water depletion and groundwater quality. This review discusses the effects of irrigation and nitrogen management practices on potato growth, yield, and quality, and their impacts on water and nitrogen use efficiencies. This review also highlights the economics and consequences of applying deficit irrigation strategies in potato production. Many researchers have demonstrated that excessive irrigation and nitrogen application rates negatively impact potato tuber yield and quality while also increasing nitrate leaching, energy consumption, and the overall costs of production. An application of light-to-moderate deficit irrigation (10–30% of full irrigation) together with reduced nitrogen rates (60–170 kg/ha) has a great potential to improve water and nitrogen use efficiencies while obtaining optimum yield and quality in potato production, depending on the climate, variety, soil type, and water availability. There is an opportunity to reduce N application rates in potato production through deficit irrigation practices by minimizing nitrate leaching beyond the crop root zone. The best irrigation and nitrogen management techniques for potato production, as discussed in this review, include using sprinkle and drip irrigation techniques, irrigation scheduling based on local crop coefficients, soil moisture content, and crop modeling techniques, applying slow-release nitrogenous fertilizers, split nitrogen application, and applying water and nitrogenous fertilizers in accordance with crop growth stage requirements.