Graphene has attracted great interest in the fields of materials science and condensed-matter physics due to its unique 2D crystal structure and its exceptionally high crystal and electronic quality. In fact, this strictly 2D carbon material also exhibits exceptional mechanical properties-including high strength, high stiffness and structural perfection-which could be comparable to that of carbon nanotubes. Recently much effort has been dedicated to the understanding of mechanical behaviors and properties of graphene. However, predicting the mechanical properties of graphene, especially by experimental methods, is still a tough challenge because of its special and tiny structures. In this paper, we critically review recent advances in the study on mechanical properties of graphene from experimental investigation, numerical simulation and theoretical analysis, respectively. We focus on the following six aspects: (1) the experimental techniques and computational approaches most often used for studying the mechanical properties of graphene, (2) the roughness and intrinsic ripples in graphene, (3) the exploration of mechanical properties such as Young's modulus, tensile and compressive strengths and bending characteristics, (4) size, temperature and strain-rate dependent mechanical behavior of graphene under tension, (5) effect of atom-scale defects and doped atoms on the mechanical behavior of graphene, and (6) the application of graphene to nanocomposites and micro/nano electrical devices. Perspective is finally given for future development of mechanics analysis of graphene and graphene-based nanostructures.