We present a review of recent advances in the statistical associating fluid theory (SAFT). In contrast to the "chemical theory", in which nonideality is explained in terms of chemical reactions between the species, SAFT and similar approaches relate nonideality to the intermolecular forces involved. Such physical theories can toe tested against molecular simulations, and improvements to the theory can be made where needed. We describe the original SAFT approach and more recent modifications to it. Emphasis is placed on pointing out that SAFT is a general method and not a unique equation of state. Applications to a wide variety of fluids and mixtures are reviewed, including aqueous mixtures and electrolytes, liquid-liquid immiscible systems, amphiphilic systems, liquid crystals, polymers, petroleum fluids, and high-pressure phase equilibria.