Acrylamide is a Class 2a carcinogen that was discovered in a variety of popular foods, including baked cereal products, in 2002. The predominant route for its formation is from free asparagine and reducing sugars in the Maillard reaction, with free asparagine concentration being the main determinant of acrylamide-forming potential in cereal products. The European Commission set “indicative” levels for acrylamide in food in 2011 and 2013, and is currently reviewing its options for further measures. Agronomic and genetic approaches to reducing the acrylamide-forming potential of wheat include the evaluation of existing varieties for low asparagine accumulation in the grain, ensuring adequate sulfur fertilization in relation to nitrogen supply, developing an understanding of the genetic control of asparagine metabolism, and identifying quantitative trait loci or molecular markers for low asparagine accumulation in the grain. Asparagine concentration in grain is affected by environmental factors (E), genetic factors (G), and interactions between the two (G × E). This paper reviews the continuing efforts being made to reduce the acrylamide-forming potential of wheat, and to increase awareness of the issue among wheat breeders, farmers, and the food industry.