Acrylamide, a chemical that is probably carcinogenic in humans and has neurological and reproductive effects, forms from free asparagine and reducing sugars during high-temperature cooking and processing of common foods. Potato and cereal products are major contributors to dietary exposure to acrylamide and while the food industry reacted rapidly to the discovery of acrylamide in some of the most popular foods, the issue remains a difficult one for many sectors. Efforts to reduce acrylamide formation would be greatly facilitated by the development of crop varieties with lower concentrations of free asparagine and/or reducing sugars, and of best agronomic practice to ensure that concentrations are kept as low as possible. This review describes how acrylamide is formed, the factors affecting free asparagine and sugar concentrations in crop plants, and the sometimes complex relationship between precursor concentration and acrylamide-forming potential. It covers some of the strategies being used to reduce free asparagine and sugar concentrations through genetic modification and other genetic techniques, such as the identification of quantitative trait loci. The link between acrylamide formation, flavour, and colour is discussed, as well as the difficulty of balancing the unknown risk of exposure to acrylamide in the levels that are present in foods with the well-established health benefits of some of the foods concerned.