To ensure the food security of future generations and to address the challenge of the ‘no hunger zone’ proposed by the FAO (Food and Agriculture Organization), crop production must be doubled by 2050, but environmental stresses are counteracting this goal. Heat stress in particular is affecting agricultural crops more frequently and more severely. Since the discovery of the physiological, molecular, and genetic bases of heat stress responses, cultivated plants have become the subject of intense research on how they may avoid or tolerate heat stress by either using natural genetic variation or creating new variation with DNA technologies, mutational breeding, or genome editing. This review reports current understanding of the genetic and molecular bases of heat stress in crops together with recent approaches to creating heat-tolerant varieties. Research is close to a breakthrough of global relevance, breeding plants fitter to face the biggest challenge of our time.