There is consistent epidemiological evidence that sleep disordered breathing and systemic arterial hypertension are deeply associated, being linked through a bidirectional complex interaction among multiple mechanisms including autonomic nervous system alterations, inflammation, hormonal and hemodynamic components, sleep alterations. However there are several unanswered questions not only from a pathophysiological perspective, but also regarding the effects of obstructive sleep apnea (OSA) treatment on arterial blood pressure values. At present, while many studies have supported the possibility to obtain at least a small blood pressure reduction with OSA treatment, in particular in hypertensive patients, large trials have not clearly confirmed a significant anti-hypertensive effect, nor a beneficial effect of this intervention on cardiovascular endpoints including cardiovascular mortality. Aim of the present review article is to address the relationship between OSA and hypertension in the light of the latest evidence in the field. Moreover we will discuss research topics which need to be investigated in the future, in order to better clarify still pending issues with the aim of obtaining an early diagnosis, a more suitable phenotyping including comorbidities, and better strategies to improve patients' compliance and adherence to treatment.