As China accelerates the implementation of the marine power strategy, the demand for advanced underwater sound-absorbing materials has become increasingly urgent. Unlike air absorption, the high hydrostatic pressure and complex marine environment impose more stringent requirements regarding underwater sound-absorbing materials. The essence of the sound absorption problem is how to efficiently transform elastic energy into heat or other forms of energy. This paper reviews the traditional underwater sound absorbing materials based on both the intramolecular friction and the energy dissipation mechanisms. The main problem of traditional underwater sound-absorbing material is attributable to its poor sound absorption performance under low frequency and high hydrostatic pressure. On the one hand, this is because the underwater sound-absorbing material is of limited thickness. Besides, due to the limitation of the mass density law, it cannot effectively absorb the low-frequency sound waves from the water. On the other hand, elastic material, such as polymer, becomes hard under high hydrostatic pressure, thus the conversion efficiency of acoustic elastic energy is greatly reduced. With the development of local resonance theory and the concept of metamaterials, a series of new underwater sound absorbing materials have been produced, which provide new ways to solve the problems encountered in developing underwater sound absorbing materials. The local resonance theory states that a small-scale structure can control the spread of long sound waves. Therefore, it can solve the problem of sound absorption at low-frequencies. This paper focuses on the theory of local resonance, the development of new sonar wood and phonon glass, and other novel underwater sound absorbing materials. Based on the local resonance theory, the phonon glass material can improve the compression performance by introducing the porous metal skeleton structure, and solve the problem of poor sound absorption performance under high hydrostatic pressure. At the end of this paper, the future development of underwater sound-absorbing materials is explored.