This paper focuses on the vulnerabilities of ADS-B, one of the avionics systems, and the countermeasures taken against these vulnerabilities proposed in the literature. Anomaly detection methods based on machine learning and deep learning algorithms among proposed countermeasures against vulnerabilities of ADS-B are analyzed in detail. The advantages and disadvantages of using an anomaly detection system on ADS-B data are investigated. Thanks to advances in machine learning and deep learning in the last decade, it has become more appropriate to use anomaly detection systems to detect anomalies in ADS-B systems. To the best of our knowledge, this is the first survey focused on studies that use machine learning and deep learning algorithms for ADS-B security. In this context; this paper addresses research on this topic from different perspectives, and draws a road map for future research, and searches for five research questions related to machine learning and deep learning algorithms used on anomaly detection systems.