The traditional sound absorption problem has not been completely resolved over the last 200 years. At every stage, its research has changed depending on practical requirements and current technologies. Phononic crystals (PCs) and acoustic metamaterials (AMs) have gained attention because of their extensive investigation and development over the past 30 years. Especially, the use of these materials brings new vitality into the traditional sound absorption problem to figure out broad working band and low-frequency absorption. This review highlights recent progress in sound absorption—from airborne to waterborne absorption—and gradient-index AMs. Progress in gradient-index AMs is singled out because of their favorable impedance matching, good viscous and thermal dissipation, and lengthened propagation paths compared with those of other materials. The progress in sound absorption of PCs and AMs is promising to serve as the next-generation sound absorbing materials, trap and reuse acoustic energy, and attenuate earthquake/tsunami wave in the future. Display omitted Acoustics; Materials Design; Materials Structure; Metamaterials