The exceptional physical properties and unique layered structure of two-dimensional (2D) materials have made this class of materials great candidates for applications in electronics, energy conversion/storage devices, nanocomposites, and multifunctional coatings, among others. At the center of this application space, mechanical properties play a vital role in materials design, manufacturing, integration and performance. The emergence of 2D materials has also sparked broad scientific inquiry, with new understanding of mechanical interactions between 2D structures and interfaces being of great interest to the community. Building on the dramatic expansion of recent research activities, here we review significant advances in the understanding of the elastic properties, in-plane failures, fatigue performance, interfacial shear/friction, and adhesion behavior of 2D materials. In this article, special emphasis is placed on some new 2D materials, novel characterization techniques and computational methods, as well as insights into deformation and failure mechanisms. A deep understanding of the intrinsic and extrinsic factors that govern 2D material mechanics is further provided, in the hopes that the community may draw design strategies for structural and interfacial engineering of 2D material systems. We end this review article with a discussion of our perspective on the state of the field and outlook on areas for future research directions.