Wheat allergy (WA) poses a diagnostic challenge due to its diverse clinical phenotypes—ranging from classic food allergy and wheat-dependent exercise-induced anaphylaxis (WDEIA) to baker’s asthma. An additional diagnostic aspect is serological cross-reactivity with grass pollen. Undoubtedly, the transition from extract-based diagnostics to precise component-based diagnostics (CRDs) facilitates the management of wheat allergy. It has significantly improved the diagnostic accuracy for WDEIA ω-5-gliadin (Tri a 19), although considering new knowledge about wheat proteins, it seems necessary to include them in the diagnostic scheme, especially where Tri a 19 remains negative despite clinical symptoms. Therefore, in this review, we evaluate the clinical utility of new wheat molecules with a high risk of anaphylaxis. We pay particular attention to Tri a 37 (α-purothionin), a thermally stable allergen associated with a 4-fold increase in the risk of severe anaphylaxis, and Tri a 36 (LMW glutenin), which shows higher sensitivity than Tri a 19 in specific pediatric cohorts. In addition, we emphasize the role of Tri a 14 (nsLTP) in distinguishing true wheat sensitization from pollen-related cross-reactivity caused by profilins (Tri a 12) or carbohydrate determinants (CCDs). Beyond diagnostics, the review discusses dynamic changes in sensitization profiles in relation to the allergic march and the phenomenon of spontaneous remission in children. New management strategies are also discussed, including the potential of omalizumab (based on the data from the OUtMATCH study) in facilitating the reintroduction of allergens into the diet.