Arterial hypertension is the leading risk factor for all stroke subtypes. However, its relationship with cognitive decline and dementia is more complex than a simple causal relationship. Cognitive functions are worse in patients with arterial hypertension, especially when the level of education is lower, age higher and arterial hypertension more severe. Arterial hypertension is an independent factor of cognitive decline. It also leads to white matter changes which contribute to the cognitive decline. Longitudinal studies have shown that a higher blood pressure at the age of 70 years is associated with an increased risk of dementia (vascular or Alzheimer) 10 to 15 years later, but blood pressure spontaneously decreases as dementia occurs. Treatments of arterial hypertension decrease the incidence of stroke, but clinical trials are still necessary to determine if they also decrease the incidence of dementia. Preliminary results obtained in elderly subjects with systolic arterial hypertension, support this hypothesis.