After the emergence of life-cycle and permanent-income consumption hypotheses, the constrained utility-maximiser model of individual behaviour became the theoretical basis of orthodox macroeconomics. This chapter will start with discussion of the random walk theory of consumption with rational expectations. It proceeds with the rise of the representative agent models (RANK), in which the consumption function consists of a representative agent maximising his/her utility over an infinite lifetime without borrowing constraints. The rise of RANK formulations was almost parallel to the gradual emergence of the new neoclassical synthesis, also known as Dynamic Stochastic General Equilibrium (DSGE) theory. There will also be a discussion of the empirical testing of the random walk theories and of their modifications in view of their empirical shortcomings. Variations of the above models with reference to consumption function, such as Heterogeneous Agent New Keynesian (HANK) and Two-Agents New Keynesian (TANK) models, will also be discussed.