Mood disorders mainly affect the patient’s daily life, lead to suffering and disability, increase the incidence rate of many medical illnesses, and even cause a trend of suicide. The glucocorticoid (GC)-mediated hypothalamus–pituitary–adrenal (HPA) negative feedback regulation plays a key role in neuropsychiatric disorders. The balance of the mineralocorticoid receptor (MR)/glucocorticoid receptor (GR) level contributes to maintaining the homeostasis of the neuroendocrine system. Consistently, a chronic excess of GC can also lead to HPA axis dysfunction, triggering anxiety, depression, memory loss, and cognitive impairment. The animal model induced by chronic corticosterone (CORT) administration has been widely adopted because of its simple replication and strong stability. This review summarizes the behavioral changes and underlying mechanisms of chronic CORT administration-induced animal models, including neuroinflammatory response, pyroptosis, oxidative stress, neuroplasticity, and apoptosis. Notably, CORT administration at different doses and cycles can destroy the balance of the MR/GR ratio to make dose-dependent effects of CORT on the central nervous system (CNS). This work aims to offer an overview of the topic and recommendations for future cognitive function research.