Epilepsy is a paroxysmal neurological disorder characterized by recurrent and unprovoked seizures affecting approximately 50 million people worldwide. Cognitive dysfunction induced by seizures is a severe comorbidity of epilepsy and epilepsy syndromes and reduces patients' quality of life. Seizures, along with accompanying histopathological and pathophysiological changes, are associated with cognitive comorbidities. Advances in imaging technology and computing allow anatomical and topological changes in neural networks to be visualized. Anatomical components including the hippocampus, amygdala, cortex, corpus callosum (CC), cerebellum and white matter (WM) are the fundamental components of seizure- and cognition-related topological networks. Damage to these structures and their substructures results in worsening of epilepsy symptoms and cognitive dysfunction. In this review article, we survey structural, network changes and topological alteration in different regions of the brain and in different epilepsy and epileptic syndromes, and discuss what these changes may mean for cognitive outcomes related to these disease states.