Advances in acoustic technology and instrumentation now make it possible to explore marine resources. As a significant component of ocean exploration, underwater acoustic target tracking has aroused wide attention both in military and civil fields. Due to the complexity of the marine environment, numerous techniques have been proposed to obtain better tracking performance. In this paper, we survey over 100 papers ranging from innovative papers to the state-of-the-art in this field to present underwater tracking technologies. Not only the related knowledge of acoustic tracking instrument and tracking progress is clarified in detail, but also a novel taxonomy method is proposed. In this paper, algorithms for underwater acoustic target tracking are classified based on the methods used as: (1) instrument-assisted methods; (2) mode-based methods; (3) tracking optimization methods. These algorithms are compared and analyzed in the aspect of dimensions, numbers, and maneuvering of the tracking target, which is different from other survey papers. Meanwhile, challenges, countermeasures, and lessons learned are illustrated in this paper.