Elucidation of the composition, functional characteristics, and formation mechanism of wheat quality is critical for the sustainable development of wheat industry. It is well documented that wheat processing quality is largely determined by its seed storage proteins including glutenins and gliadins, which confer wheat dough with unique rheological properties, making it possible to produce a series of foods for human consumption. The proportion of different gluten components has become an important target for wheat quality improvement. In many cases, the processing quality of wheat is closely associated with the nutritional value and healthy effect of the end-products. The components of wheat seed storage proteins can greatly influence wheat quality and some can even cause intestinal inflammatory diseases or allergy in humans. Genetic and environmental factors have great impacts on seed storage protein synthesis and accumulation, and fertilization and irrigation strategies also greatly affect the seed storage protein content and composition, which together determine the final end-use quality of wheat. This review summarizes the recent progress in research on the composition, function, biosynthesis, and regulatory mechanism of wheat storage proteins and their impacts on wheat end-product quality.