The correlation energy of a high density fermionic Coulomb gas, called Jellium, is expected to be given by the Gell-Mann Brueckner formula. I will discuss an analogue of this formula for the mean-field regime. I present a rigorous upper bound established by variational methods in the case of Coulomb interaction. I will further review similar results for more regular potentials, which is meanwhile well understood for particles in a fixed box. The talk is based on joint work with Martin Christiansen and P. T. Nam.