Ionic liquids (ILs) are a class of organic salts that in their pure state exist as liquids over astonishingly large temperature ranges, from just below ambient temperature to over 400 oC. In addition to having a wide liquidus range, ionic liquids possess many other intriguing physical properties including vanishingly small vapor pressure and the ability to dissolve both polar and non-polar compounds. A host of potential applications for ILs have been proposed including use in fuel cells, catalysis, as heat transfer fluids, and as (potentially) environmentally benign replacement solvents for industrial reactions and separation processes. A solid understanding of how the molecular structure of an IL affects its thermophysical properties and phase equilibrium behavior is necessary to be able to design an ionic liquid that can be used for a specific industrial task, will not pose a serious health hazard if released in a chemical spill, and can be produced in large quantities at a low cost. This problem can be addressed using computational molecular modeling methods, which provide a useful tool for studying the structure-property relationships of ILs. In this dissertation computational methods, including ab initio quantum mechanical (QM) calculations and molecular dynamics (MD) simulations are used to study a variety of ionic liquid systems, including a pure IL, an aqueous IL mixture, and mixtures of ILs with 1-butanol. The microscopic fluid structures and dynamics of the ILs and their mixtures are reported in the form of site-site radial distribution functions and association factors, and self-diffusion coefficients for the cation, anion, water and alcohol. The prediction of phase equilibrium properties of complex fluids and fluid mixtures by molecular simulation remains a challenging task. Many of the current computational methods for the prediction of phase equilibrium properties rely upon trial particle insertion/deletion steps or particle transformation steps. It is well known that particle insertions, deletions, and transformations become problematical when performed in fluids at high densities. In this dissertation a new method for the prediction of phase equilibrium is developed which relies upon gradual and dynamic particle transformations. It is shown that dynamic particle transformations are nearly an order of magnitude more efficient than standard MC-type transformations.