Negative Poisson’s ratio (NPR) (otherwise called auxetics) materials and structures feature enhanced energy absorption under cyclic loading both at low- and high-frequency excitations. We show in this paper experimental and simulation results related to open cell PU-PE foams, honeycombs, and composites, all exhibiting a negative Poisson’s ratio value. The open cell auxetic foams provide a significant damping capacity at low frequency and high preload as well as under broadband excitation compared to the conventional foams from which they are derived. We show also that the acoustic absorption properties of the auxetic foams are significantly enhanced compared to conventional PU-PE under 500 Hz, and their loss factor increased using their specific shape memory property. We describe also the vibration damping properties of NPR honeycombs with different unit cell topologies and the damping capacity of NPR carbon fiber composites under flexural cyclic loading.