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Methane is an abundant earth resource important for the energy sector. The development of better catalysts for the complete combustion of methane and the discovery of new catalysts that can directly oxidise methane to methanol are of great scientific importance. The total oxidation of methane to CO2 is considered for amorphous surface palladium oxide. A partially oxidised palladium surface is found to have both metal-like and oxide-like character. This peculiar characteristic is found to be important for increased reactivity, with dehydrogenation steps having enhanced activity on metal areas and oxidation steps having enhanced activity on oxide areas of the surface. These findings allow the further development of catalysts that stabilise the metal and oxide phase together, improving catalyst efficiency. The mechanism for the direct oxidation of methane to methanol is investigated for a Rh@ZSM-5 catalyst. The effect of molecules coordinating to the single atom centre on the reaction mechanism is explored. CO has a considerable effect as a ligand, explaining the experimental requirement for CO to have a trace presence in the system. Despite water also being required experimentally, a minimal ligand effect is found. However, water is found to be crucial as a hydrogen source for a key elementary step in the reaction. The similarity of the chemistry of single atom heterogeneous systems and homogeneous systems is discussed. These findings show the possibility of modulating ligand effects in heterogeneous catalysts. The increased reactivity of methanol against methane is investigated for a variety of fcc metals. It is found that methanol as a reactant is consistently more reactive for C-H activation, C-O coupling, and C-OH coupling. As methane and methanol have different affinities for water, the effect of an aqueous environment on the conversion-selectivity limit is considered. Water is found to not have an asymmetric effect on the reactivity of methane and methanol, mirroring the findings of the gas phase calculations. However, a C-OH mechanism is promoted in the aqueous phase, which would have a considerable effect on the selectivity on the production of methanol from methane, by minimising the formation of other oxygenates. This explains a long held mystery of why water promotes the selectivity of the methane to methanol process across many systems. The failure of palladium, a total oxidation catalyst, for the methane to methanol process is characterised and explained with a total combustion microkinetic model. A streamlined microkinetic model is designed that can accurately describe the methane to methanol formation. Excess dehydrogenation of methane is the main route of selectivity loss. Single atom alloys are then considered as a potential opportunity for a selective methane to methanol catalyst class. 64 surfaces are considered as potential catalysts, with 7 found to be indicative of being effective methane to methanol catalysts. These are then modelled for their activity and selectivity towards methanol production. One modelled catalyst has remarkably improved selectivity and activity over palladium, allowing future experimental trials which are focused on the best and most promising catalysts.