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Epilepsy is a serious and prevalent neurological disease. Epileptiform discharges (EDs), transient large-amplitude changes in electric field, are a common clinical biomarker of epilepsy and are frequently used to plan anti-epileptic surgery. However these pathological events are poorly understood, and there is still considerable debate over whether EDs enable or prevent seizures. One challenge in answering this question is that, like neuronal action potentials, EDs are event data and may possess complicated multivariate structure invisible to bivariate statistics (e.g. correlation, coherence). Point process modeling is a powerful, rigorous technique that can flexibly estimate such structure. These models have been widely used to decode action potentials but never in epilepsy. I will review some of the main ideas of point process modeling, discuss its practical advantages, and show how it can be extended to dissect the spatiotemporal structure of EDs.