Obstructive sleep apnea/hypopnea (OSAH) syndrome is a highly prevalent condition. Severe OSAH affects 2–6% of the population, although only 10% of subjects are correctly diagnosed and treated. OSAH is an important and unresolved public health care problem because of its role in the development of cardiovascular events, negative impact on quality of life, and as a cause of traffic accidents. Longitudinal and cross-sectional studies have shown a strong association between OSAH and hypertension. Moreover, a number of open-label studies, the majority of 21 controlled studies included in the present review, a systematic review, and 4 recent meta-analyses have shown a reduction of blood pressure (BP) of about 2mm Hg with continuous positive airway pressure (CPAP). This lowering of blood pressure is significant in terms of reduction of both cardiovascular and cerebrovascular risk and death. The effect is greater in hypertensive subjects and in those with more severe OSAH. Accordingly, treatment with CPAP could be considered in patients with severe OSAH and hypertension even in the absence of symptoms. The challenge to researchers is to find markers for discriminating subjects in whom blood pressure will decrease from non-responders. This will help to refine relevant clinical indicators for CPAP treatment in clinical practice.