The variational method for calculating energy of quantum fluids, and its applications to the Bose liquid 4He, Fermi neutron gas, and liquid 3He are discussed. The correlation functions are parameterized by their healing distance, and can depend on the states occupied by the correlated particles in the model wave function. They are calculated by constrained variation of lowest order contributions. The healing distance has a prescribed value in lowest order calculations, whereas it is sufficiently large in hopefully exact energy calculations. The direct many-body cluster diagrams are summed with successive approximations of an integral equation. The contribution of exchange diagrams is shown to decrease rapidly with the number of exchanges, and their sums are truncated after the energy has converged to within a few percent.