This chapter presents the main families of representation languages for preferences on combinatorial domains (composed by several attributes or variables with discrete value domains). In the first part of the chapter, we present the problem in its full generality. A large part of these languages are said to be graphical, because they work by expressing elementary preferences in a local way, using structural independence properties that are represented under the form of a graph. In the second (respectively, third) part of the chapter we review graphical languages for expressing ordinal (respectively, cardinal) preferences. Another class of preference representation languages makes use of (propositional) logic; they will be reviewed in the fourth part of the chapter, together with proper ‘preference logics’.