Mechanical metastructures have superior mechanical properties coming from the topology of special-ly designed representative elements,and have attracted wide attention due to their mathematical basis,super-normal features and broad applications.To optimize the design procedure,grasp the future trends and promote the interdisciplinary innovation,the fundamental design concepts and research advancements of mechanical metastructures were reviewed.First,the design methods for mechanical metastructures were classified based on the forward and inverse design concepts.Second,within the forward design category,the principles,appli-cable fields,and optimization directions of periodic superstructures,surface defect superstructures,and math-ematical model-based superstructures were discussed.For the reverse design category,the progresses and ex-isting problems in the application of optimization algorithms and learning algorithms in the field of mechanical metastructures were analyzed,with future challenges and open issues concluded.
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