In both research and industry, materials will be exposed to stresses, be it during fabrication, normal use, or mechanical failure. The response to external stress will have an important impact on properties, especially when atomic details govern the functionalities of the materials. This review aims at summarizing current research involving the responses of graphene and graphene materials to applied stress at the nanoscale, and to categorize them by stress-strain behavior. In particular, we consider the reversible functionalization of graphene and graphene materials by way of elastic deformation and strain engineering, the plastic deformation of graphene oxide and the emergence of such in normally brittle graphene, the formation of defects as a response to stress under high temperature annealing or irradiation conditions, and the properties that affect how, and mechanisms by which, pristine, defective, and polycrystalline graphene fail catastrophically during fracture. Overall we find that there is significant potential for the use of existing knowledge, especially that of strain engineering, as well as potential for additional research into the fracture mechanics of polycrystalline graphene and device functionalization by way of controllable plastic deformation of graphene.