Sleep apnea/hypopnea disorders include centrally originated diseases and obstructive sleep apnea (OSA). This last condition is renowned as a frequent secondary cause of hypertension (HT). The mechanisms involved in the pathogenesis of HT can be summarized in relation to two main pathways: sympathetic nervous system stimulation mediated mainly by activation of carotid body (CB) chemoreflexes and/or asphyxia, and, by no means the least important, the systemic effects of chronic intermittent hypoxia (CIH). The use of animal models has revealed that CIH is the critical stimulus underlying sympathetic activity and hypertension, and that this effect requires the presence of functional arterial chemoreceptors, which are hyperactive in CIH. These models of CIH mimic the HT observed in humans and allow the study of CIH independently without the mechanical obstruction component. The effect of continuous positive airway pressure (CPAP), the gold standard treatment for OSA patients, to reduce blood pressure seems to be modest and concomitant antihypertensive therapy is still required. We focus this review on the efficacy of pharmacological interventions to revert HT associated with CIH conditions in both animal models and humans. First, we explore the experimental animal models, developed to mimic HT related to CIH, which have been used to investigate the effect of antihypertensive drugs (AHDs). Second, we review what is known about drug efficacy to reverse HT induced by CIH in animals. Moreover, findings in humans with OSA are cited to demonstrate the lack of strong evidence for the establishment of a first-line antihypertensive regimen for these patients. Indeed, specific therapeutic guidelines for the pharmacological treatment of HT in these patients are still lacking. Finally, we discuss the future perspectives concerning the non-pharmacological and pharmacological management of this particular type of HT.