Aqueous-polymer two-phase systems consist of various combinations of water, polymer(s), low molecular weight component(s), and salts. These aqueous-polymer systems are comprised of two phases, each of which contains about 90 percent (by weight) water. Due to some very unique properties, these systems have been applied to separations involving biological molecules for at least a quarter of a century. In particular, these systems are inexpensive, efficient, and provide a mild (aqueous) and possibly stabilizing environment for fragile biologically-active molecules. These systems may also be designed for a high degree of selectivity. Although much effort has been expended in the area of polymer solution theory, the theory of why these systems exhibit this extraordinary two-phase behavior that characterizes them as viable liquid-liquid extraction systems for use with biologically-active molecules is not completely understood. A thermodynamic model which could accurately represent the phase equilibria exhibited by these systems would be useful for the design of systems for use in many different applications. A potpourri of thermodynamic models and their underlying theoretical structure have been critically studied for their particular application to predicting the phase behavior of aqueouspolymer two-phase systems. In particular, the Flory-Huggins model is reviewed (with discussion of its inadequacies and subsequent modifications); the theory of Ogston; the model by Heil; several local composition models (NRTL, Wilson, and UNIQUAC); and two group-contribution models (ASOG and UNIFAC) are all discussed. The development of a solvent-electrolyte model (Chen's model) based on local composition theory (in particular the NRTL model) is reviewed, and the subsequent possible modification of this theory for solvent-polymer-electrolyte systems is discussed. The pros and cons of each model are discussed and qualitative results are given. Quantitative comparisons with experimental data are made with several of these models when appropriate data are available. The main conclusions of this work are: 1. A major limitation to the modeling of these aqueous-polymer two-phase systems is the lack of experimental data. Sufficient, accurate data is needed for the reduction of meaningful thermodynamic parameters by which thermodynamic models can be tested for their applicability. There exists a definite need for the generation of accurate, meaningful thermodynamic data from well characterized systems. 2. The most promising model identified in this work is the theory of Ogston. First, the model is based on the virial expansion and is thus quite suitable for dilute solutions. The Ogston model is the simplest theoretically-relevant dilute-solution model. Second, it appears to be easily extended to solvent-polymer-electrolyte solutions. 3. The Flory equation of state approach appears to be promising for representing polymer solutions. The free volume dissimilarity effect on which it is based is extremely important for solvent-polymer solutions. The most important aspect of this theory is its ability to predict lower critical solution temperature (LCST) behavior -- for which the Flory-Huggins theory is totally inadequate. / M.S.