This review of the work done on the formulation and estimation of complete systems of consumer demand functions is primarily concerned with problems and issues around this topic. These issues are partly of a theoretical and partly of an empirical nature. Constraints on such systems, derived from theoretical considerations, are used to deal with the problems of lack of sufficient data, but can sometimes also be tested. Among the various alternative approaches, as yet no clear-cut choice can be made, although it appears that additivity of preferences is too restrictive.