This research programme aims to develop a new theoretical framework for modelling and analysing spatio-temporal networks. The theory developed in this programme will underpin our ability to exactly specify the structured form of network behaviour in time and space. This will advance statistical methodology and theory, unifying results from stochastic processes with network theory to do so. New technical approaches to modelling will be proposed, as well as new asymptotic large sample scenarios. As a consequence of the methodological development, new analysis techniques for applications in real-world problems will be proposed that will improve our ability to make defensible conclusions from real data sets.Modelling network data and estimating such models is challenging, especially in a modern setting, because most observed networks are very large. This leads to computational and inferential challenges. However, handling sparse and large networks is not enough to be able to describe highly structured network data. Most networks are coupled with secondary structure, and possess patterned behaviour in time and space. Linkages between nodes are frequently added and removed over time, and implicit structure is generated from latent spatial patterns.The understanding of networks must be extended to encompass spatio-temporal patterns, to quantify such structural aspects of network data. This will require combining theory and methods from different parts of mathematics, and developing new statistical theory. This project therefore aims to a) model temporally evolving networks, b) understand the characteristics of growing and decaying networks, c) model and estimate spatial and temporal characteristics in networks and d) propose new models of spatial structure. These developments will combine to form a new theoretical framework for families of networks with a rich and complex structure.