In persons showing gluten intolerance, wheat storage proteins (gliadins and glutenins) cause IgE-mediated allergies and coeliac disease. Because both of these protein fractions play a significant role in the human diet, intensive research has been carried out to explore the biochemical and molecular reasons for their allergenicity, and the possibilities for eliminating or limiting it. In spite of much progress, this problem has not been solved yet. This paper reviews important information on the structure and conformation of gluten proteins in the context of their allergenicity. Three significant protein structure elements are emphasized. The first is short (“toxic”) amino acid sequences that probably function as antibody-binding epitopes in immunological reactions. Other structural elements considered are beta turns, giving allergen particles a specific conformation, and disulphide (SS) bonds which stabilize that structure. Attempts to modify gluten proteins, using various enzyme systems and a thioredoxin reducing system, are also discussed. Such modifications may considerably decrease allergen immunoreactivity. Finally, an interdisciplinary strategy, using methods from genetics, plant breeding, food technology and medicine, is proposed which may aid in developing wheat having decreased allergenicity.