Sorghum is grown in semi-arid to arid regions of the world and serves as the staple food for about half a billion people in sub-Saharan Africa and Asia. The adaptation of grain sorghum to a wide range of environmental conditions has led to the evolution and existence of extensive genetic variation for drought tolerance. Consequently, sorghum is expected to play an increasingly important role in agriculture and meeting world food demand in the face of climate change, land degradation and increasing water scarcity. Drought is a complex phenomenon, and is considered one of the most significant factors limiting crop yields around the world and continues to be a challenge to plant breeders, despite many decades of research. Underestimating the genetics and the physiological mechanisms underlying drought tolerance is vital for the breeding to alleviate adverse effects of drought in order to boost productivity. In this literature review, research findings from the 1970s up to present are included. Most of the basic researches on the mechanism of drought tolerance were done in the early 1980s, and most of the current researches focus on verification and fine-tuning of methodologies. The paper outlines the main effects of drought on crop growth and development, and yield. It then examines the basic information on physiological mechanisms of drought in crops. Subsequent discussion is given on the genetic control of drought tolerance, and breeding methods in sorghum.