Sorghum is an important staple food crop in drought prone areas of Sub-Saharan Africa, which is characterized by erratic rainfall with poor distribution. Sorghum is a drought-tolerant crop by nature with reasonable yield compared to other cereal crops, but such abiotic stress adversely affects the productivity. Some sorghum varieties maintain green functional leaves under post-anthesis drought stress referred to as stay-green, which makes it an important crop for food and nutritional security. Notwithstanding, it is difficult to maintain consistency of tolerance over time due to climate change, which is caused by human activities. Drought in sorghum is addressed by several approaches, for instance, breeding drought-tolerant sorghum using conventional and molecular technologies. The challenge with conventional methods is that they depend on phenotyping stay-green, which is complex in sorghum, as it is constituted by multiple genes and environmental effects. Marker assisted selection, which involves the use of DNA molecular markers to map QTL associated with stay-green, has been useful to supplement stay-green improvement in sorghum. It involves QTL mapping associated with the stay-green trait for introgression into the senescent sorghum varieties through marker-assisted backcrossing by comparing with phenotypic field data. Therefore, this review discusses mechanisms of drought tolerance in sorghum focusing on physiological, morphological, and biochemical traits. In addition, the review discusses the application of marker-assisted selection techniques, including marker-assisted backcrossing, QTL mapping, and QTL pyramiding for addressing post-flowering drought in sorghum.