The focus of this work is the development and improvement of chemistry schemes in both 1D and 3D atmosphere models, applied to exoplanets. With an ever increasing number of known exoplanets, planets orbiting stars other than the Sun, the diversity in the physical and chemical nature of planets and their atmospheres is becoming more apparent. One of the prime targets, and the focus of many observational and theoretical studies, are the subclass of exoplanets termed hot Jupiters, Jovian sized planets on very short period orbits around their host star. Due to their close orbit, with orbital periods of just a few days, the atmospheres of such planets are heated to very high temperatures (~1000-2000 K) by the intense irradiation from the star. In addition, it is expected that these planets should have synchronised their rotation with their orbital period, a phenomenon called tidal-locking, that leads to a permanently illuminated dayside and a perpetually dark nightside. This combination of intense heating and tidal-locking leads to an exotic type of atmosphere that is without analogue in our own Solar system. Observational constraints suggest that some of these atmospheres may be clear whilst others may be cloudy or contain haze. Some hot Jupiters appear to be inflated with radii larger than is expected for their mass. For the warmest hot Jupiters optical absorbing species TiO and VO are expected to be present, due to the thermodynamical conditions, where they can strongly influence the thermal structure of the atmosphere, yet so far these species have remained elusive in observations. Theoretical simulations of these planets appear to provide poor matches to the observed emission flux from the nightside of the planet whilst providing a much better agreement with the observed dayside flux. These outstanding questions can be tackled in two complimentary ways. Firstly, the number of exoplanets subject to intense observational scrutiny must be increased to improve the statistical significance of observed trends. Secondly, and in tandem, the suite of available theoretical models applied to such atmospheres must be improved to allow for a more comprehensive understanding of the potential physical and chemical processes that occur in these atmospheres, as well as for better comparison of model predictions with observations. In this thesis we present the development and application of one-dimensional (1D) and three-dimensional (3D) models to the atmospheres of hot exoplanets, with a focus on improving the representation of chemistry. One of the concerns of this work is to couple the radiative transfer and chemistry calculations in a one-dimensional model to allow for a self-consistent model that includes feedback between the chemical composition and the thermal structure. We apply this model to the atmospheres of two typical hot Jupiters to quantify this effect. Implications for previous models that do not include this consistency are discussed. Another major focus is to improve the representation of chemistry in the Met Office Unified Model (UM) for exoplanet applications, a three-dimensional model with its heritage in modelling the Earth atmosphere that has recently been applied to exoplanets. We discuss the coupling of two new chemistry schemes that improve both the flexibility and capabilities of the UM applied to exoplanets. Ultimately these developments will allow for a consistent approach to calculate the 3D chemical composition of the atmosphere taking into account the effect of large scale advection, one of the processes currently hypothesised to cause the discrepancy between model predictions and observations of the nightside emission flux of many hot Jupiters.