Ionic liquids (ILs) are an intriguing class of compounds, belonging to a subset of molten ionic salts with melting points near or less than 100 ºC. There has been much excitement and promise in recent years over the possible applications of ILs, such as solvent-free-electrolyte solutions, reusable solvents for carbon dioxide capture, and energetic ionic liquids for use as explosives and propellants. Having intriguingly well-balanced intermolecular and ionic interactions, small changes in quantum-based effects (such as dispersion or charge transfer) can play important roles in IL properties. ILs are thereby challenging to model classically, and require ab initio based methods to be modeled accurately. This dissertation looks at different ab initio based approaches to modeling the interactions found in ionic liquids, and the roles fragmentation methods are filling in moving toward accurate and cost efficient methods for modeling ionic liquids.