A demand system comprises a set of demand equations, one for each good and service purchased by the consumer. This chapter starts with a discussion on the nature of demand systems associated with a consumer-optimisation problem. Then comes Engel curves, the relation between expenditure on each good and service as a function of income. These are a form of a demand system whereby all consumers pay the same set of prices, as might approximate the case with survey data of household expenditures at a given point of time. Subsequent sections present several popular demand systems: the linear expenditure system and its generalisations, the Rotterdam model, the almost ideal system and the quadratic version, and related models including the translog. The chapter concludes with a discussion of index numbers as valuable summary measures and their links with consumer demand.