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.

Novel three-dimensional (3D) continuously graded phononic crystals (CGPCs) have been designed, and fabricated by 3D printing. Each of the CGPCs is an entity instead of a combination of several other samples, and the porosity distribution of the CGPC along the incident direction is nearly linear. The sound absorption characteristics of CGPCs were experimentally investigated and compared with those of uniform phononic crystals (UPCs) and discretely stepped phononic crystals (DSPCs). Experimental results show that CGPCs demonstrate excellent sound absorption performance because of their continuously graded structures. CGPCs have higher sound absorption coefficients in the large frequency range and more sound absorption coefficient peaks in a specific frequency range than UPCs and DSPCs. In particular, the sound absorption coefficients of the CGPC with a porosity of 0.6 and thickness of 30 mm are higher than 0.56 when the frequency is 1350–6300 Hz and are all higher than 0.2 in the studied frequency range (1000–6300 Hz). CGPCs are expected to have potential application in noise control, especially in the broad frequency and low-frequency ranges.