  Cluster algebras are a class of commutative algebras whose generators are
defined by a recursive process called mutation. We give a brief introduction to
cluster algebras, and explain how discrete integrable systems can appear in the
context of cluster mutation. In particular, we give examples of birational maps
that are integrable in the Liouville sense and arise from cluster algebras with
periodicity, as well as examples of discrete Painlev\'e equations that are
derived from Y-systems.
