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The mechanical behavior of high quality two-dimensional (2D) crystals offers exciting opportunities for new material design, such as the combination of extremely high in-plane stiffness and bending flexibility, compared to existing three-dimensional (3D) material forms. By combining different 2D crystals vertically or by in-plane stitching, unusual properties can arise due to nonlinear mechanical interactions between them. Van der Waals forces between vertically stacked crystals give rise to a wide range of useful phenomena such as layer-number dependent friction, superlubricity, creasing, and spatial modulation of elastic properties through Moiré structures. In the present article, we review and explain the mechanical behavior of 2D materials and heterostructures (graphene, hexagonal boron nitride, transition metal dichalcogenides). Linear elastic properties of these 2D crystalline monolayers are well-studied using membrane nanoindentation towards their application in nano-electro-mechanical systems (NEMS) devices. On the other hand, a more thorough understanding of friction, fracture and stress transfer mechanisms between 2D layers and with the substrate or matrix is still lacking. More in-depth understanding of geometry-dependent behavior could enable the application of these materials in multi-functional composites. We discuss emerging opportunities achievable by assembling 2D heterostructures to tailor their mechanical behavior, and perhaps even break the traditional bounds limiting the properties of the bulk homostructures. Furthermore, to accelerate the design and discovery of the infinite combinations of new 2D heterostructures, we construct a crowd-sourced searchable online database to record and exploit the studies reporting on the complex arrangements of these crystals.