Drought is the most important crop production limiting factor in the changing climate scenario and its intensity is predicted to increase in future. Sunflower is an important oilseed crop having 8% share in the world oilseed production. Although, it is a moderately drought tolerant crop, severe drought causes reduction in the seed and oil production. Therefore, to ensure sustainable sunflower achene and oil production, it is very important to understand the relationship among the physiological, biochemical, genetic and agronomic basis of drought for its sustainable management. Impact of drought stress on various aspects of sunflower has been reported earlier but there is not a single study describing the physiological, biochemical and genetic basis of drought in sunflower at molecular and crop level. In this review manuscript, influence of drought on sunflower achene yield and oil quality has been analyzed critically at both cell, plant and crop level, and the possible management options to mitigate the severity of the drought stress are proposed. Available literature describing the impact of drought stress on physiological and biochemical aspects (like, photosynthesis, water relations, nutrient uptake and oxidative damage), morphological and growth parameters and achene yield and oil quality has been discussed critically. Based on the discussion on the impact of drought stress, various management strategies, such as breeding for drought tolerance (conventional or biotechnological), exogenous application of hormones and osmoprotectants, seed treatment and soil nutrient management has been reviewed and discussed. It is concluded from discussion that sunflower responds to water stress by osmotic adjustments, turgor maintenance, carbon assimilation maintenance and hormonal regulations. A comprehensive research on integration of different management options, including agronomic management, conventional breeding and modern biotechnological advances, is needed for the sustainable improvement of sunflower achene yield and oil quality under drought stress. This may also contribute significantly under a climate change scenario.