Climate change constitutes the greatest threat to food security ever seen in the history of humankind, associated mainly with the increasing number and severity of abiotic stresses (e.g., drought and heat). These climatic impacts are huge hampering factors in terms of the growth, development, and yield of crops resulting in a far-reaching economic loss that intensifies the problem of malnutrition among the debt populations. The most relevant aspect of ensuring sustainable agriculture and supplying food to an increasingly larger world population against a changing climate revolves around developing climate-resilient crops. This is a review that gives an overview of existing knowledge regarding the physiological, morphological and biochemical adaptation of crops to drought and heat stress as well as the complex genetic basis of the mechanisms behind the tolerance to stress. It also critically looks at traditional breeding methods, their achievements and their shortcomings and also the advanced strategies of genetics which are dealt with in great length. These new techniques are molecular-based breeding strategies like Marker-Assisted Selection (MAS) and Genomic Selection (GS) which utilizes the use of genetic markers to increase the rate of selection. Besides, the review explains the revolutionary nature of genetic engineering and genome editing as a technology (e.g., CRISPR/Cas9) capability that can be undertaken to specifically target and leverage genes to strengthen stress tolerance. High-throughput phenotyping has been mentioned as an integrative technology with the next generation omics technologies including: genomics, transcriptomics, proteomics, and metabolomics to address the synergistic need to identify new genes, the complex signaling pathways involved in stress response, and to conduct more accurate breeding. They have been used to produce stress-tolerant varieties as shown by case studies on major crops such as rice, wheat, maize, and legumes with the practical application and effect. Challenges do exist even though much improvement has been achieved, such as the polygenic nature of traits associated with tolerance, the interaction between a given genotype and environmental factors, and an effective phenotyping platform. Future outlooks base the need to develop multidisciplinary, integrated solutions through a combination of conventional and molecular technologies with systems biology and digital agriculture to provide resilient and sturdy, widely adapted, and enduring climate-resilient crops. The report highlights the importance of a coordinated international effort towards research and development so that agricultural systems can be reinforced to withstand the unavoidable effects of climate change.