Cluster-tilted algebras were introduced by Buan, Marsh and Reiten. These algebras arise as endomorphism algebras of cluster-tilting objects in a cluster category. A cluster-tilted algebra can be constructed explicitly by a quiver with relations, where the relations are uniquely determined by its quiver (a result of Buan, Iyama, Reiten and Smith). In this talk, we shall give an introduction to cluster categories and cluster-tilted algebras.We shall also provide an explicit description of cluster-tilted algebras of type~$\tilde{A}_n$. Time permitting, we shall give a derived equivalence classification for such algebras.