Abstract: Lattice grids are new-type materials with high specificstiffness and specific strength. The topologies of the 2D periodic lattices are analyzed together with their manufacturing methods. Equivalent continuummethods to obtain effective stiffness, strength and yield surfaces arediscussed, including the micropolar elastic theory of the latticestructures. The size effect and influence of soft or rigid inclusions are analyzed. The fracture mechanics analysis on the cellulargrids shows that the triangular and hexagonal grids are flawsensitive, while the Kagome lattices are damage tolerant. The latticegrids may be classified into grid structures,grid stiffened structures and grid sandwich structures. The failure modes,the optimzation principles and the experiment results are discussed indetails. The recent work of the authors on carbon fiber reinforced latticematerials are also introduced.