Despite their economic importance and growing demand, concerns are emerging around wheat-based foods and human health. Most wheat-based foods are made from refined white flour rather than wholemeal flour, and the overconsumption of these products may contribute to the increasing global prevalence of chronic diseases, particularly type 2 diabetes and obesity. Here, we review how the amount, composition and interactions of starch and cell wall polysaccharides, the major carbohydrate components in refined wheat products, impact human health. We discuss strategies and challenges to manipulate these components for improved diet and health using newly developed wheat genomics tools and resources. Commercial foods developed from these novel approaches must be produced without adverse effects on cost, consumer acceptability and processing properties.