It is the aim of this thesis to provide a rigorous and comprehensive analysis of single cell gene expression data. Specifically, the focus is on expression of the human Prolactin gene, which can be measured in intact tissue samples via a reporter process. To do this, we develop a robust statistical procedure, the stochastic switch model, to model the transcriptional regulation within single cells that properly accounts for both intrinsic and extrinsic variability whilst also incorporating a realistic measurement process. The stochastic switch model provides a highly exible framework for coupling the regulatory system without the need for detailed prior knowledge of the underlying regulatory mechanisms. In this thesis, this methodology is applied to numerous datasets to find different regulatory behaviour evident in different biological conditions. Moreover, since the data provided has in addition a representative spatial resolution, we investigate how the spatial organisation of the expressing cells changes in these different biological conditions. This is achieved via spatial point processes and makes use of the recently developed hybrid Gibbs processes. The thesis ends by revisiting the transcriptional regulation within single cells and how analysing these processes in space reveals evidence of cell signalling. From this evidence, various semi-mechanistic models are derived with attention focused on model identifiability. Consequently, this thesis provides both methods and analysis for the temporal, the spatial and the spatio-temporal data regarding single cell gene expression.