Sleep apnea-hypopnea syndrome (SAHS) is a chronic and highly prevalent disease considered a major health problem in industrialized countries. The gold standard diagnostic methodology is in-laboratory nocturnal polysomnography (PSG), which is complex, costly, and time consuming. In order to overcome these limitations, novel and simplified diagnostic alternatives are demanded. Sleep scientists carried out an exhaustive research during the last decades focused on the design of automated expert systems derived from artificial intelligence able to help sleep specialists in their daily practice. Among automated pattern recognition techniques, artificial neural networks (ANNs) have demonstrated to be efficient and accurate algorithms in order to implement computer-aided diagnosis systems aimed at assisting physicians in the management of SAHS. In this regard, several applications of ANNs have been developed, such as classification of patients suspected of suffering from SAHS, apnea-hypopnea index (AHI) prediction, detection and quantification of respiratory events, apneic events classification, automated sleep staging and arousal detection, alertness monitoring systems, and airflow pressure optimization in positive airway pressure (PAP) devices to fit patients' needs. In the present research, current applications of ANNs in the framework of SAHS management are thoroughly reviewed.