Wheat is an important staple food globally, providing a significant contribution to daily energy, fiber, and micronutrient intake. Observational evidence for health impacts of consuming more whole grains, among which wheat is a major contributor, points to significant risk reduction for diabetes, cardiovascular disease, and colon cancer. However, specific wheat components may also elicit adverse physical reactions in susceptible individuals such as celiac disease (CD) and wheat allergy (WA). Recently, broad coverage in the popular and social media has suggested that wheat consumption leads to a wide range of adverse health effects. This has motivated many consumers to avoid or reduce their consumption of foods that contain wheat/gluten, despite the absence of diagnosed CD or WA, raising questions about underlying mechanisms and possible nocebo effects. However, recent studies did show that some individuals may suffer from adverse reactions in absence of CD and WA. This condition is called non‐celiac gluten sensitivity (NCGS) or non‐celiac wheat sensitivity (NCWS). In addition to gluten, wheat and derived products contain many other components which may trigger symptoms, including inhibitors of α‐amylase and trypsin (ATIs), lectins, and rapidly fermentable carbohydrates (FODMAPs). Furthermore, the way in which foods are being processed, such as the use of yeast or sourdough fermentation, fermentation time and baking conditions, may also affect the presence and bioactivity of these components. The present review systematically describes the characteristics of wheat‐related intolerances, including their etiology, prevalence, the components responsible, diagnosis, and strategies to reduce adverse reactions.