In this thesis mathematical techniques and models are applied to electroencephalographic (EEG) recordings to study mechanisms of idiopathic generalised epilepsy (IGE). First, we compare network structures derived from resting-state EEG from people with IGE, their unaffected relatives, and healthy controls. Next, these static networks are combined with a dynamical model describing the ac- tivity of a cortical region as a population of phase-oscillators. We then examine the potential of the differences found in the static networks and the emergent properties of the dynamic network as individual biomarkers of IGE. The emphasis of this approach is on discerning the potential of these markers at the level of an indi- vidual subject rather than their ability to identify differences at a group level. Finally, we extend a dynamic model of seizure onset to investigate how epileptiform discharges vary over the course of the day in ambulatory EEG recordings from people with IGE. By per- turbing the dynamics describing the excitability of the system, we demonstrate the model can reproduce discharge distributions on an individual level which are shown to express a circadian tone. The emphasis of the model approach is on understanding how changes in excitability within brain regions, modulated by sleep, metabolism, endocrine axes, or anti-epileptic drugs (AEDs), can drive the emer- gence of epileptiform activity in large-scale brain networks. Our results demonstrate that studying EEG recordings from peo- ple with IGE can lead to new mechanistic insight on the idiopathic nature of IGE, and may eventually lead to clinical applications. We show that biomarkers derived from dynamic network models perform significantly better as classifiers than biomarkers based on static network properties. Hence, our results provide additional ev- idence that the interplay between the dynamics of specific brain re- gions, and the network topology governing the interactions between these regions, is crucial in the generation of emergent epileptiform activity. Pathological activity may emerge due to abnormalities in either of those factors, or a combination of both, and hence it is essential to develop new techniques to characterise this interplay theoretically and to validate predictions experimentally.