Grain legumes are important sources of proteins, essential micronutrients and vitamins and for human nutrition. Climate change, including drought, is a severe threat to grain legume production throughout the world. In this review, the morpho-physiological, physio-biochemical and molecular levels of drought stress in legumes are described. Moreover, different tolerance mechanisms, such as the morphological, physio-biochemical and molecular mechanisms of legumes, are also reviewed. Moreover, various management approaches for mitigating the drought stress effects in grain legumes are assessed. Reduced leaf area, shoot and root growth, chlorophyll content, stomatal conductance, CO2 influx, nutrient uptake and translocation, and water-use efficiency (WUE) ultimately affect legume yields. The yield loss of grain legumes varies from species to species, even variety to variety within a species, depending upon the severity of drought stress and several other factors, such as phenology, soil textures and agro-climatic conditions. Closure of stomata leads to an increase in leaf temperature by reducing the transpiration rate, and, so, the legume plant faces another stress under drought stress. The biosynthesis of reactive oxygen species (ROS) is the most detrimental effect of drought stress. Legumes can adapt to the drought stress by changing their morphology, physiology and molecular mechanism. Improved root system architecture (RSA), reduced number and size of leaves, stress-induced phytohormone, stomatal closure, antioxidant defense system, solute accumulation (e.g., proline) and altered gene expression play a crucial role in drought tolerance. Several agronomic, breeding both conventional and molecular, biotechnological approaches are used as management practices for developing a drought-tolerant legume without affecting crop yield. Exogenous application of plant-growth regulators (PGRs), osmoprotectants and inoculation by Rhizobacteria and arbuscular mycorrhizal fungi promotes drought tolerance in legumes. Genome-wide association studies (GWASs), genomic selection (GS), marker-assisted selection (MAS), OMICS-based technology and CRISPR/Cas9 make the breeding work easy and save time in the developmental cycle to get resistant legumes. Several drought-resistant grain legumes, such as the chickpea, faba bean, common bean and pigeon pea, were developed by different institutions. Drought-tolerant transgenic legumes, for example, chickpeas, are developed by introgressing desired genes through breeding and biotechnological approaches. Several quantitative trait loci (QTLs), candidate genes occupying drought-tolerant traits, are identified from a variety of grain legumes, but not all are under proper implementation. Hence, more research should be conducted to improve the drought-tolerant traits of grain legumes for avoiding losses during drought.