Ionic liquids (ILs) - salts that melt near room temperature - have remarkable properties as solvents for a wide variety of molecules and ions. ILs share with water the rare ability to promote formation of surfactant micelles and lipid bilayer membranes, but some also display amphiphilic (surfactant-like) character. We will examine the structure of mixtures of ionic liquids with water and with model amphiphilic compounds such as ethanol and octanol. This will enable us to understand the intermolecular forces that drive self-assembly by ionic liquids and by other molecules in ionic liquids, and also how this compares with self-assembly in water. These mixtures have widespread applications, ranging from drug delivery systems to foods to polymer composites and filtration membranes. Understanding their molecular arrangements, will enable improvements in the next generation of applications.