  Q-systems first appeared in the analysis of the Bethe equations for the
XXX-model and generalized Heisenberg spin chains. Such systems are known to
exist for any simple Lie algebra and many other Kac-Moody algebras. We
formulate the Q-system associated with any simple, simply-laced Lie algebras g
in the language of cluster algebras, and discuss the relation of the
polynomiality property of the solutions of the $Q$-system in the initial
variables, which follows from the representation-theoretical interpretation, to
the Laurent phenomenon in cluster algebras.
