A wealth of longitudinal epidemiologic evidence links high blood pressure or hypertension to cognitive decline and incident dementia. Some (but not all) studies have suggested that antihypertensive treatment is beneficial, reducing risk of decline and dementia. There are plausible mechanisms to support the possibility that hypertension may increase the risk of dementia. There is also evidence suggesting that the two dementia types thought to be most common, Alzheimer's disease and vascular dementia, have overlapping risk factors. Seven placebo-controlled trials of antihypertensive treatment have assessed cognitive function, incident dementia, or both, with mixed outcomes. The Hypertension in the Very Elderly Trial (HYVET), despite showing reductions in mortality and stroke with active treatment, found no significant reduction of incident dementia, although the trial was stopped early. Meta-analyses used to explore this area further are inconclusive, and comparative trials are now required.