The aim of the paper is to discuss the main characteristics exhibited by so-called rigid designators. Identification of proper names and some descriptions with rigidly designating expressions almost became a truism in the philosophy of language. It is argued that proper names are rigid designators because their reference is conventional, direct and nondescriptive but descriptions are such in spite of their reference being descriptive and mediated. Certain kinds of rigid designators and rigid reference are discriminated and it is found that unlike rigidly designating descriptions most of proper names must be tied to the idea of transworld reference in order to be rigid. The conclusion is that rigidly designating descriptions must be metaphysically loaded much more than proper names for the former presuppose a kind of essentialism.