A sustainable livestock economy depends on both production and consumption, inextricably linked in local, national and global markets. At each scale, technical innovation and production practices need to respond to evolving demand for both market and non-market attributes of livestock systems. This review considers recent and evolving demand-side challenges focussing on emerging preferences related to environmental, dietary and health impacts, arising from both production and consumption. It suggests that these attributes need to be integral to any definition of high-producing animal systems. This discussion is mostly framed using neoclassical economic theory, which highlights market failure and the role of negative and positive external effects or social costs. It examines how our understanding of the demand for these attributes is evolving, leading to market segmentation in some cases, and an existential threat to livestock production as consumption decisions change, investors seek to avoid potential liabilities related to greenhouse gas emissions and potentially antimicrobial resistance, and governments intervene to control other undesirable social costs. The discussion distinguishes between market imperatives in high- and lower-income countries, and how income and consumption trajectories may be less deterministic in a more hyperlinked world where product information may accelerate the evolution of preferences towards and away from livestock products. The review acknowledges the limits of a neoclassical approach, drawing attention to more fundamental concepts of biophysical limits to growth and value pluralism, which indicates values (e.g. intrinsic) that lie beyond the neoclassical framing of demand and value.