Hypertension is one of the principal risk factors for cerebrovascular diseases. Several epidemiologic studies have also indicated a positive correlation between cognitive decline or dementia and blood pressure level. Indeed, the results of most longitudinal studies show that cognitive functioning is often inversely proportional to blood pressure values measured 15 or 20 years previously. Cerebral infarcts, lacunae, and white matter changes are implicated in the pathogenesis of vascular dementia, but may also favor the development of Alzheimer's disease. Microcirculation disorders and endothelial dysfunctions are also advanced to explain the deterioration in cognitive functions in hypertensive subjects. Data from recent therapeutic trials open the way to the prevention of dementia (vascular or Alzheimer's type) by antihypertensive treatments and must be confirmed by other studies.