Underwater acoustics has been implemented mostly in the field of sound navigation and ranging (SONAR) procedures for submarine communication, the examination of maritime assets and environment surveying, target and object recognition, and measurement and study of acoustic sources in the underwater atmosphere. With the rapid development in science and technology, the advancement in sonar systems has increased, resulting in a decrement in underwater casualties. The sonar signal processing and automatic target recognition using sonar signals or imagery is itself a challenging process. Meanwhile, highly advanced data-driven machine-learning and deep learning-based methods are being implemented for acquiring several types of information from underwater sound data. This paper reviews the recent sonar automatic target recognition, tracking, or detection works using deep learning algorithms. A thorough study of the available works is done, and the operating procedure, results, and other necessary details regarding the data acquisition process, the dataset used, and the information regarding hyper-parameters is presented in this article. This paper will be of great assistance for upcoming scholars to start their work on sonar automatic target recognition.