Progressive population aging is determining that the spectrum of clinical manifestations of cognitive deterioration reaches epidemic proportions. At the present time, there are not available treatments that can modify the natural history of the different nosologies that determine a progressive lost of cognitive functions. In the last years, several vascular risk factors have been established as risk factors for cognitive deterioration. Arterial hypertension, by its prevalence, possibility of treatment, and control, emerges as a potentially modifiable risk factor for the deterioration of cognitive function. This review updates the knowledge of the impact of arterial hypertension in cognitive function, analyzing its physiopathological consequences in tissues and cerebral vessels with implications in cognitive function.