Conventionally, tuning materials' properties can be done through strategies such as alloying, doping, defect engineering, and phase engineering, while in fact mechanical straining can be another effective approach. In particular, elastic strain engineering (ESE), unlike conventional strain engineering mainly based on epitaxial growth, allows for continuous and reversible modulation of material properties by mechanical loading/unloading. The exceptional intrinsic mechanical properties (including elasticity and strength) of two-dimensional (2D) materials make them naturally attractive candidates for potential ESE applications. Here, we demonstrated that using the strain effect to modulate the physical and chemical properties toward novel functional device applications, which could be a general strategy for various 2D materials and their heterostructures. We then show how ultralarge, uniform elastic strain in free-standing 2D monolayers can permit deep elastic strain engineering (DESE), which can result in fundamentally changed electronic and optoelectronic properties for unconventional device applications. In addition to monolayers and van der Waals (vdW) heterostructures, we propose that DESE can be also applied to twisted bilayer graphene and other emerging twisted vdW structures, allowing for unprecedented functional 2D material applications.