Hydrogen bonds are of great interest in the solid state due to their importance in structural, functional and dynamical properties of chemical systems. Moderate hydrogen bonds have been linked with proton transfer, whereas the short, strong hydrogen bonds enable proton migration. Previous work in our group on relatively simple hydrogen bonded adducts relied on the combination of ab initio computational modelling (molecular dynamics) with variable temperature diffraction results (X-ray and neutron). These demonstrated that the interplay of these techniques was successful in studying the phenomena of proton transfer and migration. The present work follows on from that, and focuses on the effects of temperature and pressure on proton transfer and migration using both experimental and computational methods. The systems studied continue to encapsulate adducts with N…O and O…O hydrogen bonds. The study of the adduct formed between squaric acid and 4,4’-bipyridine was found to exhibit proton transfer associated with a single-crystal to single-crystal phase transition at 450 K that is coupled to a colour change (yellow to red). X-ray and neutron diffraction initially revealed the heavy atom structure and secondly the location of the hydrogen atoms along the moderate N…O hydrogen bond (ca. 2.6 Å). Computational modelling supported this and deduced the reason for the striking colour change. Pressure studies also determined that the adduct underwent two phase-transitions with a similar colour change, indicating that proton transfer is also a factor here, but with powder patterns different from the high temperature form, indicating that further polymorphs for this interesting system must exist. In an attempt to lower the temperature at which proton transfer would occur the base was changed to one of a more basic nature, i.e. co-crystallisation of squaric acid and 2,2’-dimethyl–4,4’-bipyridine was pursued. This lead to the formation of two red crystals that were found to posses the base doubly protonated at all temperatures studied (from 300 K to 100 K). The adduct of N,N-dimethylurea with phosphoric acid was obtained from a systematic study designed to follow the success of a previously reported system that showed proton migration (the adduct of urea and phosphoric acid). The new material was found to crystallise as the 2:1 adduct and maintained the short, strong hydrogen bonds characteristic of the parent structure. As part of the systematic approach undertaken throughout the research presented here, co-crystallisation of a combination of acids and bases were attempted in order to synthesise new materials containing short, strong hydrogen bonds. These yielded the adducts between oxalic acid and 2,2’-dimethyl-4,4’-bipyridine, and oxamic acid and 4,4’-bipyridine. In addition to these adducts some compounds ended up reacting to create new ones, e.g. the fusing of dimethyl urea and squaric acid to give N-(2-hydroxycyclobutene-3,4-dione)-N’,N’-dimethylurea and N-(2- hydroxycyclobutene-3,4-dione)-N,N'-dimethylurea, while a new polymorphs of one of the precursors on its own was also obtained (N,N’-dimethylurea). The resulting co-crystallisations did not all follow the design quite as intended. They did, however, yield interesting new structures, some of which have the potential to be proton migration and transfer systems.