Two-dimensional (2D) materials, such as Graphene, hBN and MoS2, are promising candidates in a number of advanced functional and structural applications, owing to their exceptional electrical, thermal and mechanical properties. Understanding mechanical properties of 2D materials is critically important for their reliable integration into future electronic, composite and energy storage applications. However, it has been a significant challenge to quantitatively measure mechanical responses of 2D materials, due to technical difficulties in the nanomechanical testing of atomically thin membranes. In this talk, we will report our recent effort to determine the engineering relevant fracture toughness of graphene with pre-existing defects, rather than the intrinsic strength that governs the uniform breaking of atomic bonds in perfect graphene. Strategies on how to improve the fracture resistance in graphene, and the implications of the effects of defects on mechanical properties of other 2D atomic layers will be discussed.