Epileptic seizures constitute a complex multiscale phenomenon that is characterized by synchronized hyperexcitation of neurons in neuronal networks. Recent progress in understanding pathological seizure dynamics provides crucial insights into underlying mechanisms and possible new avenues for the development of novel treatment modalities. Here we review some recent work that combines in vivo experiments and computational modeling to unravel the pathophysiology of seizures of cortical origin. We particularly focus on how activity-dependent changes in extracellular potassium concentration affects the intrinsic dynamics of neurons involved in cortical seizures characterized by spike/wave complexes and fast runs.