Straws and stovers are often called ‘by-products’ of grain production even though they are increasingly important, e.g. for animal feed, thatching, soil improvement, mushroom production and industrial use. As a result, plant breeders, agronomists, economists and animal nutritionists have to pay more attention than before to the total value of crops, i.e. whole plant value in which straws and grain both play a part. This paper reviews literature about the technical potential of breeding and/or management for more or better straw. It then discusses issues of the economic value (EV) and nutritional value (NV) of straw and stovers for livestock feed to guide research and development in cereal breeding and management. It is mainly based on experiences from the Indian subcontinent and semi-arid regions of the Near and Middle East. The paper shows that the quantity and quality of straw produced has changed considerably over recent decades as a result of breeding policies, new cultivation patterns and choice of cultivars. Both EV and NV depend on type of grain, animal production system and access to other feeds. A classification of these factors is provided and suggests that the EV of straw is particularly important in low-input systems with stovers from coarse grains.