Despite its global importance and increasing consumption, wheat is a focus of debate about the relationship between diet and health. This concern relates to the fact that the vast majority of wheat products are made from refined white flour rather than whole grains or wholemeal flour, and hence contribute to the increasing prevalence of chronic diseases, particularly type 2 diabetes and obesity. In this review we focus on starch and cell wall polysaccharides, the major carbohydrate components of refined white flour. We discuss how their amounts, compositions and interactions in refined wheat products determine impacts on health. We also discuss how these components can be manipulated using new wheat genomics tools and resources to improve health outcomes. Finally, we stress that this must be achieved without adverse effects on cost, consumer acceptability and processing properties.