Humans need sleep. It is important for physical and psychological recreation. During sleep our consciousness is suspended or least altered. Hence, our ability to avoid or react to disturbances is reduced. These disturbances can come from external sources or from disorders within the body. Obstructive Sleep Apnea (OSA) is such a disorder. It is caused by obstruction of the upper airways which causes periods where the breathing ceases. In many cases, periods of reduced breathing, known as hypopnea, precede OSA events. The medical background of OSA is well understood, but the traditional diagnosis is expensive, as it requires sophisticated measurements and human interpretation of potentially large amounts of physiological data. Electrocardiogram (ECG) measurements have the potential to reduce the cost of OSA diagnosis by simplifying the measurement process. On the down side, detecting OSA events based on ECG data is a complex task which requires highly skilled practitioners. Computer algorithms can help to detect the subtle signal changes which indicate the presence of a disorder. That approach has the following advantages: computers never tire, processing resources are economical and progress, in the form of better algorithms, can be easily disseminated as updates over the internet. Furthermore, Computer-Aided Diagnosis (CAD) reduces intra- and inter-observer variability. In this review, we adopt and support the position that computer based ECG signal interpretation is able to diagnose OSA with a high degree of accuracy.