The integrity of gas pipelines is important for fuel delivery, but pipeline leaks frequently occur for a variety of reasons. As a result, pipeline leak detection for gas pipelines is now an important issue of concern. Currently, there is an absence of review regarding the development of pressure wave-based method for detecting leaks in gas pipelines. Therefore, this paper surveys the published research articles in related fields in recent decades. The principles and applications of leak detection based on pressure wave are categorized. Different signal analysis and machine learning techniques utilized in the detection of leakage are surveyed. In addition, the localization range, localization capability (size of the leak), and localization error of different methods are investigated in detail. The advantages, limitations, and performance of different detection methods are discussed, and potential future directions are proposed. This will be beneficial to experts and engineers working in this area of expertise.