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Since the success of monolayer graphene exfoliation, two-dimensional (2D) materials have been extensively studied due to their unique structures and unprecedented properties. Among these fascinating studies, the most predominant focus has been on their atomic structures, defects, and mechanical behaviors and properties, which serve as the basis for the practical applications of 2D materials. In this review, we first highlight the atomic structures of various 2D materials and the structural and energy features of some common defects. We then summarize the recent advances made in experimental, computational, and theoretical studies on the mechanical properties and behaviors of 2D materials. We mainly emphasized the underlying deformation and fracture mechanisms and the influences of various defects on mechanical behaviors and properties, which boost the emergence and development of topological design and defect engineering. We also further introduce the piezoelectric and flexoelectric behaviors of specific 2D materials to address the coupling between mechanical and electronic properties in 2D materials and the interactions between 2D crystals and substrates or between different 2D monolayers in heterostructures. Finally, we provide a perspective and outlook for future studies on the mechanical behaviors and properties of 2D materials.

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