Chapter 1 gives an introduction to hydrogen bonding and the existing research surrounding short strong hydrogen bonds. The concept of a reversible, temperature dependent, proton migration is introduced and a selection of systems in which this proton migration has been observed to date is discussed. Chapter 2 describes the synthetic techniques, characterisation methods and computational procedures used throughout this work. Chapter 3 describes the variable temperature structural studies on 3,5 pyridinedicarboxylic acid and its deuterated analogues. The fully deuterated analogue undergoes a non-classical, first order, isosymmetric phase transition between 150 and 200 K and DFT calculations have identified vibrational free energy changes as the driving force for this. Although similar behaviour is exhibited by two partially deuterated isotopologues, no such transition is observed in the fully protonated form. Chapter 4 presents a combined spectroscopic and computational study of three isotopologues of 3,5-pyridinedicarboxylic acid. Whilst spectral observations and diffraction data are coincident for the fully deuterated form, the advantage of spectroscopy over diffraction for describing migration in the fully protonated and a partially deuterated isotopologue is demonstrated. Chapter 5 explores the role of vibrational coordinates in the PES governing proton dynamics in light of NMR relaxometry measurements, which reveal a non zero dynamical rate at temperatures close to 0 K, indicative of proton tunnelling. Tunnelling is confirmed by the presence of a 2-well potential in the system, and described based on reorganisations within the structure as a whole. Chapter 6 reports the synthesis of further short strong hydrogen bond systems. The variable temperature structural properties for each of these compounds are discussed, and comparisons with other well known proton migration compounds are drawn. Chapter 7 presents the attempted synthesis of a series of new co-crystals, with components based on those of 4-methylpyridine-pentachlorophenol; the successful products were found to possess medium length hydrogen bonds. Variable temperature diffraction studies for one of these products are discussed and show that it undergoes a phase transition on cooling resulting from slight rotations of its components. Chapter 8 gives the main conclusions of this thesis and outlines a number of opportunities for further work.