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Sleep apnea (SA) is one of the most prevalent sleep-related problems, impacting more than 100 million people worldwide. A full-night Polysomnography (PSG) is an effective SA diagnosis strategy. However, it requires multiple wearable devices and the patient staying overnight to collect the findings, rendering it both a time-consuming and costly option. Research attempts to develop non-invasive, sensor-based, or automated solutions for diagnosing SA are also made in recent years. In this study, we analyzed a total of 85 papers, shortlisted from an initial collection of 954 articles published in reputable scientific repositories, e.g., IEEE Xplore, PubMed Central (PMC), Springer, Elsevier etc., where each chosen study was thoroughly examined to determine its contribution and performance. A detailed analysis of data preprocessing, feature extraction and classification algorithm is also addressed. It is found that most of the studies are based on signal analysis for identifying sleep apnea, which yields results with substantial reliability, while contemporary research emphases have been on heart rate variability and pulse oximetry outcomes.