The relationships between the brain and arterial hypertension are strong. The brain, through the hypothalamus, can quickly adapt the blood pressure level to maintain the cerebral blood flow. An acute increase in blood pressure, if it overtakes the autoregulatory capacities, needs an urgent intervention to decrease neurological problems such as encephalopathy. In chronic situations, arterial hypertension is a frequent cause of stroke, either ischemic or hemorragic, both in patients free and those who have already suffered from brain damage. Hypertension is also an actor in the genesis of vascular, but also Alzheimer's dementia. A strict control of blood pressure (but also in other atherosclerotic risk factors) into the normal range is needed to protect the brain, and this is more important than the choice of a particular class of antihypertensive agents, except the betablockers. The risk starts from the normal values of blood pressure.