Various lattice statistical-thermodynamic theories after E.A. Guggenheim [Guggenheim, 1952] have been proposed with different assumptions on nonrandomness, the explicitness of the solution, and the model parameters. During the last decade, the present authors proposed a general approximation tool to the quasichemical solution of the nonrandom lattice-fluid combinatory and formulated a new rigorous EOS and the improved versions including the unified group contribution extensions and systems with strong association. In this study, developments of those EOSs are discussed with emphasis of on the practical utility of each model.