Mechanical metamaterial composed of chiral honeycomb structure is high performance engineering materials developed in recent years. They have the advantages of light weight, high specific stiffness, negative Poisson' s ratio, adjustable structural parameters and stable mechanical properties. It not only can realize the dual mechanical functions of in-plane deformation and out-of-plane load-bearing, but also has excellent engineering application performance such as vibration isolation and sound absorption and noise reduction and control of elastic wave propagation. It has great potential in the fields of intelligent structure, vehicle, ship, aerospace and so on. Two mechanical aspects of its elastic properties and impact resistance were reviewed. First, the progress of theoretical analysis and research on the elastic properties such as the surface poplar modulus, negative Poisson's ratio, and elastic properties of external shear modulus of mechanical metamaterials were reviewed and commented. Further, in the aspect of impact resistance, the overall deformation and impact resistance of the existing chiral honeycomb mechanical metamaterials under impact load were reviewed based on perspectives of model establishment and finite element analysis. Finally, it was pointed out that in the further research of elasticity and impact properties, the mechanical model of internal ligament deformation and force transmission can be further established and the energy absorption mechanism of the impact process to be further explored so as to provide the reference for the optimization design of the internal structure of ligaments and node rings in this type of metamaterial.