Climate change has resulted in extreme events becoming more frequent, intense, and destructive. It is essential to understand the behaviour of extreme weather processes for societal preparedness. This thesis focuses on the development of spatio-temporal statistical models for extremely hot summer and cold winter temperature events in Ireland, in the context of climate change. To provide reliable estimates of extreme temperatures of unobserved magnitudes, we rely on asymptotically justified extrapolations provided by extreme value theory. Modelling observational weather records is problematic for several reasons. Firstly, these data tend to have low spatial resolution and contain spatial bias. This thesis presents a framework to unify information about spatial extreme events using both historical temperature observations and output from climate models to enrich the statistical model’s topographic information while addressing spatial bias. Secondly, observational weather records are incomplete, with sites having different record lengths as well as missing values. To deal with this issue we develop a spatial extreme value model which allows for an estimation of the full dependence structure without imputing or removing spatial observations that are not fully observed. We identify a lack of a unified measure of extremity in the spatio-temporal context. Such tools are critical for practitioners to summarise and present risks associated with non-stationary spatio-temporal extremal processes. To address this gap in the literature, we develop several novel summary tools to synthesise and visually communicate non-stationarity in the extreme values of spatio-temporal processes. We apply our methodology to analyse the extremal behaviour of both summer maximum and winter minimum daily temperatures in Ireland. We characterise changes on a marginal level (i.e., the behaviour at any location in Ireland) as well as on a spatial level. For the marginal model, we use spatial covariates derived from climate model outputs and explore several potential temporal covariates. To model the spatial extremal dependence, we use an r-Pareto process with H¨usler- Reiss margins in order to incorporate incomplete spatial observations and apply our measures of spatio-temporal non-stationarity to simulations from our fitted model of summer and winter extreme temperatures.