Several recent advances have led to accurate equations of state for linear and branched chain polyatomic fluids. One of these equations of state, the Statistical Associating Fluid Theory, SAFT, proposed by Chapman et al. [W.G. Chapman, G. Jackson, K.E. Gubbins, Mol. Phys. 65 (1988) 1057-1079; W.G. Chapman, K.E. Gubbins, G. Jackson, M. Radosz, I&EC Research 29 (1990) 1709-1721], enables engineers to predict the effects of chain length, intermolecular association, and compressibility on phase behavior for mixtures containing solvents, monomers, and polymers. The utility of SAFT is a result of its basis in statistical mechanics in the form of Wertheim's thermodynamic perturbation theory. This basis in theory also allows us to systematically improve or extend the equation of state. In this paper, we briefly discuss the physical basis for the SAFT approach. Examples of applications of the equation of state are presented for mixtures of solvents, monomers, and polymers. Opportunities to improve the equation of state and to extend its range of applicability also are discussed.