Understanding physicochemical properties of ionic liquids is important for their rational use in extractions, reactions, and other applications. Ionic liquids are not simple fluids: their ions are generally asymetric, flexible, with delocalized electrostatic charges, and available in a wide variety. It is difficult to capture their subtle properties with models that are too simplistic. Molecular simulation using atomistic force fields, which describe structures and interactions in detail, is an excellent tool to gain insights into their liquid-state organization, how they solvate different compounds, and what molecular factors determine their properties. The identification of certain ionic liquids as self-organized phases, with aggregated nonpolar and charged domains, provides a new way to interpret the solvation and structure of their mixtures. Many advances are the result of a successful interplay between experiment and modeling, possible in this field where none of the two methodologies had a previous advance.