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The focus of this thesis is on using mechanical strain to tailor the electronic properties of graphene. The first half covers the electro-mechanical coupling for graphene in different configurations, namely a hexagonal Y-junction, various shaped bubbles on different substrates, and with kirigami cuts. For all of these cases, a novel combination of tight-binding electronic structure calculations and molecular dynamics is utilized to demonstrate how mechanical loading and deformation impacts the resulting electronic structure and transport. For the Y-junction, a quasi-uniform pseudo magnetic field induced by strain restricts transport to Landau-level and edge-state-assisted resonant tunneling. For the bubbles, the shape and the nature of the substrate emerge as decisive factors determining the effectiveness of the nanoscale pseudo magnetic field tailoring in graphene. Finally, for the kirigami, it is shown that the yield and fracture strains of graphene, a well-known brittle material, can be enhanced by a factor of more than three using the kirigami structure, while also leading to significant enhancements in the localized pseudo magnetic fields. The second part of the thesis focuses on dissipation mechanisms in graphene nanomechanical resonators. Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta, and Ulam (FPU). Using molecular dynamics and continuum modeling of a ring-down setup, it is shown that thermalization due to nonlinear mode coupling intrinsically limits the quality factor of nanomechanical graphene drums and turns them into potential test beds for FPU physics. The relationship between thermalization rate, radius, temperature and prestrain is explored and investigated.