In the past decade there has been rapidly growing interest in ionic liquids, molten salts that melt near room temperature. Interest in these compounds is due to their unique properties, especially their negligible vapor pressure and unique solvent characteristics. There has been a concerted effort to measure the physical properties and phase behavior of ionic liquids and ionic liquid mixtures and gain a deeper understanding of the unique behaviors of ionic solvents. In addition, there have been numerous theoretical studies to predict properties of ionic liquids and explore the underlying physical interactions that influence ionic liquid properties. In this study, two separate methods are used to predict properties of ionic liquids and investigate the fundamental relationships between molecular structure and chemical properties. The quantitative structure-property relationship (QSPR) method combines experimental data with statistical techniques to construct functional relationships between molecular structures and physical properties. This method is used to create predictive relationships for melting point and limiting solubility behavior of ionic liquids. The resulting structure-property relationships provide a deeper understanding of how the molecular structure of ionic liquids influences their properties. In addition, these numerical relationships are shown to be useful in predicting properties of new compounds. Molecular simulation uses relationships from statistical thermodynamics to determine bulk properties of a system based on the molecular level interactions of the system. The key link is the energetic model, or force field, which describes the interactions between molecules. One problem in molecular simulation of particular interest is determining the phase behavior of a system based on the energetic model of the system. Solid-liquid equilibrium is particularly challenging due to the nature of the solid phase and the solid-liquid transition. In this study, a new methodology is developed to evaluate solid-liquid equilibrium for complex molecular systems in a general way using molecular simulation. This method is validated against two simple atomic systems and applied to two molecular systems. The results indicate how strongly a system's force field can influence phase coexistence and this analysis can be a stringent test of a force field's ability to model a system's interactions.