Since iron (Fe) and zinc (Zn) are essential micronutrients for human immunity and metabolic activities, it is important to biofortify major food crops such as wheat and improve the bioavailability of Fe and Zn. In this review, we focused on analyzing studies conducted to identify and evaluate QTLs, genes, and associated molecular markers related to Fe and Zn content in wheat, their absorption mechanisms, and bioavailability in terms of genetics and breeding. Because bread wheat has a limited Fe and Zn content in its grains, many studies have used wild, synthetic, or mutant wheat resources with high Fe and Zn contents. Many studies have been conducted to characterize related genes, of which Gpc-B1 is the major gene that increases the final content of Fe, Zn, and protein in association with an Gpc-B1 increase in Fe uptake and regulate Zip and YSL expression. Research determining the appropriate phytic acid content and increasing phytase activity to improve bioavailability was also highlighted.