Over the past decades, we have seen an increase in the availability of data that includes spatial information. Incorporating spatial information in models may result in performance improvements, which may then be used to better inform decision-making processes. When modelling spatial data, typical assumptions such as independence of observations across locations, no longer hold. As a consequence, careful methodology is required. This thesis addresses the modelling of two common types of data encountered in spatial modelling: measurements of a quantity at pre-specified locations (e.g., sensor measurements), and events for which geographical location and time are recorded. We develop effective approaches for modelling spatial data in an interpretable manner, thus making it suitable for application domains where the transparency of a model is a desired property. We demonstrate the developed approaches with empirical simulation studies.