Nature has always represented a fundamental source of inspiration to solve mankind's scientific challenges and engineering tasks. For instance, it has been shown that a hierarchical organization over multiple length scales allows enhanced quasi-static mechanical properties, while the relative orientation of adjacent chiral centers may affect the physical properties of a polymer, and internal heterogeneous architectures may result in shape changing systems, to cite a few examples. In this paper, we discuss some examples of how bio-inspiration may be used to enhance the potential of phononic crystals and acoustic metamaterials in terms of vibration attenuation and control of wave propagation.