In this thesis, I present three main results which demonstrate significant development in the field of exoplanet atmosphere detection and modelling. A model for estimating the distortion of hot-Jupiter exoplanets due to the gravitational attraction by the host star solely based on observable parameters of transiting systems. The most significant case of distortion is that of the exoplanet WASP-12b which shows a bulk density over-estimation of 12%. In order to investigate the systematic sources of error associated with ground-based observations, the secondary eclipse of the transiting hot- Jupiter WASP-19b was observed, and found to have an eclipse depth of O.88±O.19mmag based on a single observation. Whilst this does represent a significant result, the systematics present in the data support further observations to better constrain the depth, duration and timing of the secondary eclipse. The final result presented in this thesis is a pilot study of the technique of 'defocussed transmission spectroscopy', a method of observation which is designed to allow for the detection of elements in the atmospheres of transiting extra-solar planets from groundbased platforms. I present limits on the detectability of sodium in exoplanet atmospheres, and provide a detailed investigation into the systematics associated with this novel observing technique. I also make recommendations as to how future observations can be improved, and present a possible detection of sodium in the atmosphere of WASP-12b with an absorption depth of O.12±O.03%.