This paper surveys some basic results on the representation of consumer preferences using duality methods. It has been prepared for inclusion in the forthcoming Handbook of Utility Theory. It is aimed at graduate students who have a solid background in economics but have not seen too much about this topic. The main purpose of the paper is to show how learning something about duality methods can make utility analysis much easier. To emphasise this, an optimal tax example is given at the beginning of the survey. The usual representations are discussed: the cost function; the indirect utility function; the distance function and the profit function. Examples of the use of each are given. The emphasis everywhere is on how quick and easy many duality methods are; relatively little attention is paid to mathematical detail.