Hypoxic-ischemic brain damage often results from a combination of cardiogenic and respiratory failure. Whether or not hypoxia in the absence of ischemia is injurious to the brain has been a topic of research. An example of hypoxia without ischemia is found in obstructive sleep apnea (OSA), which causes recurrent nocturnal oxygen desaturations. Furthermore, it is a pervasive problem in the general population, particularly in people with common disorders such as obesity or diabetes. Mounting evidence in the past decade indicates that cerebrovascular disease, specifically stroke, and neurobehavioral consequences, including excessive daytime sleepiness and cognitive deficits, are prevalent in people with OSA, at great costs to the individual well-being, public health, and the economy. Investigation of the two disease associations poses similar and unique challenges. Predictors of these sequelae need to be better defined. The apnea-hypopnea index, the most common measure of OSA, has proven to be variably related to stroke and cognitive impairment. The role of individual markers, whether they are comorbidities or differences in inherent cognitive reserve, also is incompletely understood. This review discusses the burgeoning literature on the neurological and neurobehavioral sequelae of OSA and highlights the future avenues of research in the field.