Hydrogen bonding (H-bonding) is an important and very general phenomenon. H-bonding is part of the basis of life in DNA, key in controlling the properties of water and ice, and critical to modern applications such as crystal engineering, catalysis applications, pharmaceutical and agrochemical development. H-bonding also plays a significant role for many ionic liquids (IL), determining the secondary structuring and affecting key physical parameters. ILs exhibit a particularly diverse and wide range of traditional as well as non-standard forms of H-bonding, in particular the doubly ionic H-bond is important. Understanding the fundamental nature of the H-bonds that form within ILs is critical, and one way of accessing this information, that cannot be recovered by any other computational method, is through quantum chemical electronic structure calculations. However, an appropriate method and basis set must be employed, and a robust procedure for determining key structures is essential. Modern generalised solvation models have recently been extended to ILs, bringing both advantages and disadvantages. QC can provide a range of information on geometry, IR and Raman spectra, NMR spectra and at a more fundamental level through analysis of the electronic structure.