  We review some recent progress on applications of Cluster Expansions. We
focus on a system of classical particles living in a continuous medium and
interacting via a stable and tempered pair potential. We review the cluster
expansion in both the canonical and the grand canonical ensemble and compute
thermodynamic quantities such as the pressure, the free energy as well as
various correlation functions. We derive the equation of state either by
performing inversion of the density-activity series or directly in the
canonical ensemble. Further applications to the liquid state expansions and the
relevant closures are discussed, in particular their convergence in the gas
regime.
