This review article provides a comprehensive overview of the mechanics and mechanical properties of two-dimensional (2D) materials, with a focus on graphene and other 2D materials such as transition metal dichalcogenides (TMDs) and hexagonal boron nitride (h-BN). The authors highlight the importance of mechanics in understanding the behavior of 2D materials, both experimentally and theoretically, and discuss the coupling between mechanical properties and other physical properties like thermal, electronic, and optical properties. The review is divided into five sections, covering elastic properties, inelastic properties, coupling with other physical properties, interfacial properties, and potential applications. In the elastic properties section, the authors discuss the experimental methods used to measure in-plane elastic properties, including nanoindentation and pressurized blister tests, and theoretical predictions from first-principles calculations and continuum mechanics models. They also address the challenges in measuring the bending modulus of 2D materials and the impact of thermal rippling on elastic properties. The inelastic properties section explores the effects of defects such as vacancies, dislocations, and grain boundaries on the strength and toughness of 2D materials. It discusses the mechanisms of toughening and the role of out-of-plane deformation in fracture. The coupling with other physical properties section examines how mechanical deformation influences the thermal, electronic, and optical properties of 2D materials, highlighting the potential for strain engineering and the effects of pseudomagnetic fields, phase transitions, and piezoelectricity. The interfacial properties section focuses on the mechanical interactions between 2D materials and substrates, including adhesion and friction, and the underlying mechanisms. The final section outlines potential applications of 2D materials in large-scale manufacturing, flexible electronics, and biomedical fields, and provides an outlook for future research in the mechanics and mechanical properties of 2D materials.This review article provides a comprehensive overview of the mechanics and mechanical properties of two-dimensional (2D) materials, with a focus on graphene and other 2D materials such as transition metal dichalcogenides (TMDs) and hexagonal boron nitride (h-BN). The authors highlight the importance of mechanics in understanding the behavior of 2D materials, both experimentally and theoretically, and discuss the coupling between mechanical properties and other physical properties like thermal, electronic, and optical properties. The review is divided into five sections, covering elastic properties, inelastic properties, coupling with other physical properties, interfacial properties, and potential applications. In the elastic properties section, the authors discuss the experimental methods used to measure in-plane elastic properties, including nanoindentation and pressurized blister tests, and theoretical predictions from first-principles calculations and continuum mechanics models. They also address the challenges in measuring the bending modulus of 2D materials and the impact of thermal rippling on elastic properties. The inelastic properties section explores the effects of defects such as vacancies, dislocations, and grain boundaries on the strength and toughness of 2D materials. It discusses the mechanisms of toughening and the role of out-of-plane deformation in fracture. The coupling with other physical properties section examines how mechanical deformation influences the thermal, electronic, and optical properties of 2D materials, highlighting the potential for strain engineering and the effects of pseudomagnetic fields, phase transitions, and piezoelectricity. The interfacial properties section focuses on the mechanical interactions between 2D materials and substrates, including adhesion and friction, and the underlying mechanisms. The final section outlines potential applications of 2D materials in large-scale manufacturing, flexible electronics, and biomedical fields, and provides an outlook for future research in the mechanics and mechanical properties of 2D materials.