Hypertension is one of the most prevalent vascular risk factors and a leading cause of disability and mortality worldwide. The negative impact of hypertension on brain health is substantial. Already well-established as a risk factor for cerebrovascular disease, hypertension also has been shown to increase the risk for cognitive impairment and dementia. Mounting evidence from epidemiological studies suggests that hypertension, particularly in midlife, is associated with late-life cognitive impairment and the development of dementia. The link between late-life hypertension and cognitive function is, however, less clear. Experimental and neuroimaging studies have revealed complexities of mechanisms underlying the link between hypertension and cognitive function. Furthermore, the effect of blood pressure lowering on cognitive function, the optimal target and timing of the intervention, and the optimal antihypertensive agent in the context of cognitive function remain unclear. In this review, we discuss contemporary science on the link between hypertension and cognitive function by reviewing experimental, neuroimaging, and life-course observational studies. Furthermore, we provide a detailed review of randomized clinical trials addressing the effect of blood pressure lowering on cognitive function. Finally, unanswered questions, challenges, and other considerations for blood pressure lowering are highlighted.