The representation dimension of an algebra was introduced by Maurice Auslander in the 70's of the last century with the aim of measuring how far an algebra is to be representation-finite. Recall that an algebra A is representation finite provided there are only finitely many non-isomorphic indecomposable finitely generated A-modules. However, more than 25 years passed before it was considered again in the mainframe of the Representation Theory of Algebras. We shall give a very quick survey on the development of such notion and discuss some recent results in a joint work with I. Assem and H. Wagner.