Phononic crystals (PCs) and elastic metamaterials (MMs) are generally defined as periodic structures exhibiting exotic vibrational properties currently unavailable in Nature (frequency band gap, waveguiding, topological protection, etc). In recent years, PCs and MMs are more and more included as emerging solutions in different fields, from structural health monitoring to sound / vibration insulation, to cite a few.In this talk, starting from the unconventional assumption that the working principle behind metamaterials is already exploited in Nature, I will present examples of bio-inspired designs of metamaterials with the aim of discussing their potential advantages (and unavoidable limitations) in terms of dynamic / static performance with respect to conventional ones. I will finally discuss potential fields of application (namely, nondestructive evaluation, waveguiding, sound insulation, etc.).