The effect of high temperature stress on wild and spring wheats is reviewed. Wild wheats include species in the genera Aegilops L. and Triticum L. Species exist in a polyploid series, diploid, tetraploid and hexaploid, based on the genome formula, n = x = 7 chromosomes. Commercial durum wheat is tetraploid with the genome formula BBAA, while bread wheat is hexaploid (BBAADD). Wheats grown at Riverside, California, from June to October exhibit heat stress at the vegetative and reproductive stages. Under high temperatures (28/15ºC day/night) during the vegetative stage, many diploid species do not grow well. Wild diploid T. urartu (AA) and T. monococcum ssp. boeoticum (AA) exhibited more effects of heat stress than the goat grasses A. speltoides (SS = BB?) or A. tauschii (DD). Wild tetraploid T. turgidum L. ssp. dicoccoides Korn (BBAA) exhibited more vegetative-phase stress tolerance than the diploid wheats. Modern Mexican cultivars of durum and bread wheats showed good establishment under high field temperatures, but often tiller number was reduced, and the developmental stages were reduced in time. All the spring durum and bread wheats tested flowered and set seed. They produced anthers with fertile pollen, and they had reproductive heat tolerance. Many wild Aegilops and Triticum accessions did not boot for lack of vernalisation, or they showed reproductive heat stress. Ten wild accessions, including A. speltoides, A. longissima and A. searsii, showed normal vegetative and reproductive development and were considered heat tolerant. They came from the same geographic area in Palestine which should be searched for landraces of wheats that show heat tolerance.