Cluster algebras appears as the coordinate ring of many interesting objects. We recall the notion of a cluster ensemble which consists of a cluster A variety and its corresponding cluster X variety. The compatible Poisson structures on these spaces are log-canonical. We construct the symplectic groupoid of the log-canonical Poisson structure on each cluster chart, and lift the cluster mutations to groupoid mutations. If time permits, I will also explain the work by Fock-Goncharov on quantization of cluster X-varieties and how it might fit into the groupoid framework. This is joint work with Dylan Rupel.