Epilepsy - the condition of recurrent, unprovoked seizures - is a common brain disease, affecting 1% of the world’s population. Seizures are typically identified as abnormal patterns in brain voltage activity. Many open questions surround epilepsy and seizures, and identifying the associated answers promises new insights for treatment and prevention. In this talk, we will consider brain voltage activity during seizure as observed at multiple spatial scales. We will show how techniques from mathematics and statistics can be used to characterize these data, identify common features, and connect observed brain activity to mechanisms. We will first examine how brain electrical activity couples and decouples during the the course of a seizure. We will then focus on a specific, open question in epileptology: why do seizures spontaneously terminate? Through analysis of human brain electrical activity at various spatial scales, we will propose that seizures self-terminate via a common dynamical mechanisms: a discontinuous critical transition or bifurcation. In contrast, prolonged seizures (status epilepticus) repeatedly approach, but do not cross, the critical transition. To support these results, we will also consider a computational model to demonstrate that alternative stable attractors, representing the seizure and post-seizure states, emulate the observed brain dynamics. These results suggest that self-terminating seizures end through a common dynamical mechanism. This description constrains the specific biophysical mechanisms underlying seizure termination, suggests a dynamical understanding of status epilepticus, and demonstrates an accessible system for studying critical transitions in nature.