Explorations into the organisation of spontaneous activity within the brain have demonstrated the existence of networks of temporally correlated activity, consisting of brain areas that share similar cognitive or sensory functions. These so-called resting state networks (RSNs) emerge spontaneously during rest and disappear in response to overt stimuli or cognitive demands. In recent years, the study of RSNs has emerged as a valuable tool for probing brain function, both in the healthy brain and in disorders such as schizophrenia, Alzheimer’s disease and Parkinson’s disease. However, analyses of these networks have so far been limited, in part due to assumptions that the patterns of neuronal activity that underlie these networks remain constant over time. Moreover, the majority of RSN studies have used functional magnetic resonance imaging (fMRI), in which slow fluctuations in the level of oxygen in the blood are used as a proxy for the activity within a given brain region. In this thesis we develop the use of magnetoencephalography (MEG) to study resting state functional connectivity. Unlike fMRI, MEG provides a direct measure of neuronal activity and can provide novel insights into the temporal dynamics that underlie resting state activity. In particular, we focus on the application of non- stationary analysis methods, which are able to capture fast temporal changes in activity. We first develop a framework for preprocessing MEG data and measuring interactions within different RSNs (Chapter 3). We then extend this framework to assess temporal variability in resting state functional connectivity by applying time- varying measures of interactions and show that within-network functional connectivity is underpinned by non-stationary temporal dynamics (Chapter 4). Finally we develop a data driven approach based on a hidden Markov model for inferring short lived connectivity states from resting state and task data (Chapter 5). By applying this approach to data from multiple subjects we reveal transient states that capture short lived patterns of neuronal activity (Chapter 6).