Maintenance of brain function depends on a constant blood supply. Deficits in cerebral blood flow are linked to cognitive decline, and they have detrimental effects on the outcome of ischemia. Hypertension causes alterations in cerebral artery structure and function that can impair blood flow, particularly during an ischemic insult or during periods of low arterial pressure. This review will focus on the historical discoveries, novel developments, and knowledge gaps in 1) hypertensive cerebral artery remodeling, 2) vascular function with emphasis on myogenic reactivity and endothelium-dependent dilation, and 3) blood-brain barrier function. Hypertensive artery remodeling results in reduction in the lumen diameter and an increase in the wall-to-lumen ratio in most cerebral arteries; this is linked to reduced blood flow postischemia and increased ischemic damage. Many factors that are increased in hypertension stimulate remodeling; these include the renin-angiotensin-aldosterone system and reactive oxygen species levels. Endothelial function, vital for endothelium-mediated dilation and regulation of myogenic reactivity, is impaired in hypertension. This is a consequence of alterations in vasodilator mechanisms involving nitric oxide, epoxyeicosatrienoic acids, and ion channels, including calcium-activated potassium channels and transient receptor potential vanilloid channel 4. Hypertension causes blood-brain barrier breakdown by mechanisms involving inflammation, oxidative stress, and vasoactive circulating molecules. This exposes neurons to cytotoxic molecules, leading to neuronal loss, cognitive decline, and impaired recovery from ischemia. As the population ages and the incidence of hypertension, stroke, and dementia increases, it is imperative that we gain a better understanding of the control of cerebral artery function in health and disease.