Obstructive sleep apnea causes intermittent hypoxia and sleep fragmentation and affects at least 20% of individuals after the age of 65. There is accumulating evidence that obstructive sleep apnea may impact brain structure and function. Recent cohort studies suggest that it is a risk factor for stroke, mild cognitive impairment and Alzheimer’s disease. Because prevention through treatment of risk factors is currently the main intervention for reducing the incidence of dementia, how obstructive sleep apnea affects brain health and whether its treatment can slow neurodegeneration are relevant questions. This Perspective Article presents the most recent findings on the neurocognitive consequences of obstructive sleep apnea in the elderly. We focus on the aging brain and the link between obstructive sleep apnea, brain health, cognitive decline and dementia. We present how new discoveries from animal models, human sleep experiments, and Alzheimer’s disease biomarkers point to an active role of disturbed sleep in dementia pathogenesis. We show preliminary data on how sex, genetics, physical exercise and cognitive reserve can strengthen or weaken the association between obstructive sleep apnea and dementia. We present preliminary results of obstructive sleep apnea treatment, which can slow, stop or reverse neurodegenerative processes accentuated by obstructive sleep apnea, even in individuals already affected by a neurodegenerative disease. We propose future research directions that include studies on mild/moderate untreated obstructive sleep apnea, the evaluation of continuous positive airway pressure treatment to slow neurodegeneration and follow-up studies of older patients that measure predictors/markers of dementia