Hypertension is a highly prevalent risk factor for stroke and dementia, and is the greatest risk factor for small-vessel disease - a frequent cause of lacunar infarction and intracerebral haemorrhage. Lacunar and cortical strokes contribute to the development of dementia in patients with, and in those without, Alzheimer disease pathology; this relationship between stroke and dementia is probably mediated by ischaemia-induced neuroinflammation. Antihypertensive treatment can reduce the risk of stroke and dementia, but requires optimal blood pressure targets to be established for individual patients. Although the rate of treatment and control of hypertension has improved markedly over the past two decades, many physicians remain reluctant to prescribe antihypertensive medication to elderly patients owing to potential adverse events such as cardiovascular morbidity and postural hypotension. In this article we argue that, in patients of all ages, not treating hypertension is a missed opportunity to prevent some of the most prevalent brain diseases.