Increasing temperature and consequent changes in climate adversely affect plant growth and development, resulting in catastrophic loss of wheat productivity. For each degree rise in temperature, wheat production is estimated to reduce by 6%. A detailed overview of morpho-physiological responses of wheat to heat stress may help formulating appropriate strategies for heat-stressed wheat yield improvement. Additionally, searching for possible management strategies may increase productivity and sustainability of growing wheat. The major findings from this review are as follows: (1) heat stress significantly reduces seed germination and seedling growth, cell turgidity, and plant water-use efficiency; (2) at a cellular level, heat stress disturbs cellular functions through generating excessive reactive oxygen species, leading to oxidative stress; (3) the major responses of wheat to heat stress include the enhancement of leaf senescence, reduction of photosynthesis, deactivation of photosynthetic enzymes, and generation of oxidative damages to the chloroplasts; (4) heat stress also reduces grain number and size by affecting grain setting, assimilate translocation and duration and growth rate of grains; (5) effective approaches for managing heat stress in wheat include screening available germplasm under field trials and/or employing marker-assisted selection, application of exogenous protectants to seeds or plants, mapping quantitative trait locus conferring heat resistance and breeding; (6) a well-integrated genetic and agronomic management option may enhance wheat tolerance to heat. However, the success of applying various techniques of heat stress management requires greater understanding of heat tolerance features, molecular cloning, and characterization of genes. The overall success of the complex plant heat stress management depends on the concerted efforts of crop modelers, molecular biologists, and plant physiologists.