Heat stress (HS) is one of the major abiotic stresses affecting the production and quality of wheat. Rising temperatures are particularly threatening to wheat production. A detailed overview of morpho-physio-biochemical responses of wheat to HS is critical to identify various tolerance mechanisms and their use in identifying strategies to safeguard wheat production under changing climates. The development of thermotolerant wheat cultivars using conventional or molecular breeding and transgenic approaches is promising. Over the last decade, different omics approaches have revolutionized the way plant breeders and biotechnologists investigate underlying stress tolerance mechanisms and cellular homeostasis. Therefore, developing genomics, transcriptomics, proteomics, and metabolomics data sets and a deeper understanding of HS tolerance mechanisms of different wheat cultivars are needed. The most reliable method to improve plant resilience to HS must include agronomic management strategies, such as the adoption of climate-smart cultivation practices and use of osmoprotectants and cultured soil microbes. However, looking at the complex nature of HS, the adoption of a holistic approach integrating outcomes of breeding, physiological, agronomical, and biotechnological options is required. Our review aims to provide insights concerning morpho-physiological and molecular impacts, tolerance mechanisms, and adaptation strategies of HS in wheat. This review will help scientific communities in the identification, development, and promotion of thermotolerant wheat cultivars and management strategies to minimize negative impacts of HS.