Absence epilepsy is a non-convulsive type of epilepsy characterized by the sudden loss of awareness. It is associated with thalamo-cortical impairment, which may cause neuropsychiatric and neurocognitive problems. Rats with spontaneous absence-like seizures are widely used as in vivo genetic models for absence epilepsy; they display behavioral and cognitive problems similar to epilepsy in humans, such as genetic absence epilepsy rats from Strasbourg (GAERS) and Wistar Albino rats from Rijswijk (WAG/Rij). Depression- and anxiety-like behaviors were apparent in GAERS, but no anxiety and depression-like symptoms were found in WAG/Rij rats. Deficits in executive functions and memory impairment in WAG/Rij rats, i.e., cognitive comorbidities, were linked to the severity of epilepsy. Wistar rats can develop spontaneous seizures in adulthood, so caution is advised when using them as a control epileptic strain. This review discusses challenges in the field, such as putative high emotionality in genetically prone rats, sex differences in the expression of cognitive comorbidities, and predictors of cognitive problems or biomarkers of cognitive comorbidities in absence epilepsy, as well as the concept of "the cognitive thalamus". The current knowledge of behavioral and cognitive comorbidities in drug-naive rats with spontaneous absence epilepsy is beneficial for understanding the pathophysiology of absence epilepsy, and for finding new treatment strategies.