The concept of Acoustic Source Identification (ASI), which refers to the process of identifying noise sources has attracted increasing attention in recent years. The ASI technology can be used for surveillance, monitoring, and maintenance applications in a wide range of sectors, such as defence, manufacturing, healthcare, and agriculture. Acoustic signature analysis and pattern recognition remain the core technologies for noise source identification. Manual identification of acoustic signatures, however, has become increasingly challenging as dataset sizes grow. As a result, the use of Artificial Intelligence (AI) techniques for identifying noise sources has become increasingly relevant and useful. In this paper, we provide a comprehensive review of AI-based acoustic source identification techniques. We analyze the strengths and weaknesses of AI-based ASI processes and associated methods proposed by researchers in the literature. Additionally, we did a detailed survey of ASI applications in machinery, underwater applications, environment/event source recognition, healthcare, and other fields. We also highlight relevant research directions.