Metamaterials can break through the performance boundaries of traditional materials through artificial structure design, and show unique advantages in the fields of impact resistance, energy absorption and lightweight. Firstly, the definition of metamaterials and their classification were introduced. Secondly, by integrating both non-gradient and gradient design concepts, the two-dimensional and three-dimensional negative Poisson[DK]’s ratio structures along with their mechanical properties were systematically sorted out. The study specifically highlighted the defects and optimization design methods of the traditional concave hexagonal honeycomb structures, the development and mechanical properties of the three-dimensional non-gradient negative Poisson[DK]’s ratio structures, as well as the design concept and superior mechanical properties of gradient negative Poisson[DK]’s ratio structures, etc. Finally, the research status of negative Poisson[DK]’s ratio metamaterials was summarized, and the possible future research directions of this material were prospected: 1) Conduct research on the mechanical properties of negative Poisson[DK]’s ratio structures under multi-physical field coupling conditions; 2) Explore the anti-impact mechanism of three-dimensional negative Poisson[DK]’s ratio structures under multiple working conditions; 3) Carry out gradient optimization design of three-dimensional negative Poisson[DK]’s ratio structures; 4) Combine with advanced manufacturing technologies to realize the integrated design and manufacturing from structure to function.