The minimum energy requirement of a distillation sets a lower, thermodynamically defined operating limit, which is increasingly important in practice due to growing interest in saving energy. During the conceptual design phase this energy information can also be used to quickly compare distillation configurations. This paper gives a summary of the most important methods published to date for the calculation of the minimum energy requirement. Firstly, the occurrence of so-called pinch zones will be systematically described. These are sections of the column in which at minimum reflux an infinite number of separation stages would be necessary. Then exact and approximating solutions of the problems both for ideal and for nonideal mixtures will be discussed. For ideal mixtures a rapid calculation is possible using the well-known Underwood equations, which can also be applied to complex columns (e.g., several feeds and side products, side stream strippers and enrichers). However, strongly nonideal multicomponent mixtures still require time-consuming simulations of columns having large numbers of plates. In such cases serious convergence problems must often be reckoned with. Recent developments aim at avoiding column simulations and at calculating pinch points directly.