Arterial hypertension (HTN) is associated with significant changes in the structure of cerebral vessels. There is a close relationship between the functional activity of neurons and the intensity of their blood supply. Vascular dementia is a heterogeneous group of diseases resulting from the pathology of neurons, glia and vessels. Cognitive disorders are the most typical manifestations of brain pathology in vascular dementia and include memory impairment, decreased learning ability, lack of personal opinion, violation of emotional control and social behavior. The article overviews the data on the organization of cerebral circulation and the mechanisms of its changes in HTN. The article analyzes the causes leading to brain hypoperfusion in elevated blood pressure. The authors discuss the mechanisms resulting in cognitive disorders in hypertensive subjects. We also address the question arising in relation of HTN and cognitive impairments: “To which extent blood pressure should be lowered in hypertensive patients with cognitive decline?”.