Audio steganography is the process of hiding a message inside an audio container. This study aims to present a systematic review of audio steganography methods. Existing reviews of audio steganography suffer from a high overlap or a low segregation level among the methods reviewed due to poor classification criteria. These articles are also lacking in terms of depth of analysis and the number of articles reviewed. The data collection method includes surveying five databases, namely, Web of Science, IEEE Explore, ScienceDirect, Scopus, and Springer, resulting in a total of 134 articles. The review focuses on the embedding process of each method. The methods can be classified into several categories based on the most prominent idea in the embedding process; hence, a new classification is proposed. The proposed classification provides a scope for summarizing and understanding the most followed approaches in audio steganography. This study then critically reviews the strengths and weaknesses of each method on the basis of its embedding behavior. Other issues on the domain of embedding, carrier types, and evaluation environments are also discussed.