Modern concepts and theories have created the ability to predict the thermodynamic properties of high-temperature liquid solutions (molten salts, metals, and slags) and vapors. These advances have made it possible to calculate thermodynamic properties and total chemistries for many technologically and scientifically important systems. Specific theories include (1) a cycle for accurately calculating the solubility products of relatively insoluble salts in reciprocal molten salt systems, (2) the coordination cluster theory, which allows one to predict the temperature and concentration dependence of the activities of a dilute solute in a multicomponent system, (3) the conformal ionic-solution theory, which predicts the properties of reciprocal and additive multicomponent molten salt systems, (4) the modified quasi-chemical theory, which predicts the properties of multicomponent silicate (and other polymeric) systems, (5) a simple extension of polymer theory, which leads to methods for predicting the sulfide capacities (as well as capacities for PO 3Ϫ 4 , SO 2Ϫ 4 , Cl Ϫ , Br Ϫ , I Ϫ , etc.) in molten silicates and other polymeric solvents, and (6) a dimensional theory for the prediction of nonelectronic entropies and free-energy functions of vapor molecules. These accomplishments have helped to create computer programs which can calculate realistic total chemistries of complex systems and have provided a method of extending the scope of fundamental thermodynamic databases of vapors.