This article provides an overview of the literature on consumer and demand system analysis with emphasis on complete food demand systems. It presents theoretical foundations, constrained utility maximization, properties, and general demand restrictions. It discusses dual functions, including the expenditure function, the indirect utility function, and the distance function. The first three dual approaches are standard tools of the applied demand system analyst. Then it introduces the issue of welfare effects and integrability along with separability and aggregation. The article also provides a review of functional forms and covers econometric issues that include estimation, inference and hypothesis testing, specification tests, and other empirical issues. Models of the almost ideal demand and inverse systems as well as some additional hypothesis tests and inferences regarding model performance are estimated and reported.