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This dissertation investigates the effect of grain boundaries (GBs) in polycrystalline graphene on the tensile fracture behavior and thermal conductivity of the graphene sheets. Current techniques to fabricate large-scale graphene intrinsically introduce defects, e.g., GBs, resulting in polycrystalline graphene sheets. Though GBs in graphene are expected to affect the mechanical properties of graphene, mechanistic understanding and quantitative determination of such effects are far from mature. For example, existing studies on the effect of GBs on the tensile behavior of graphene only focus on a twin GB perpendicular to the tensile loading direction. However, GBs in a polycrystalline graphene sheet under uniaxial tension could be subject to tension in any arbitrary directions, depending on the GB and grain orientation in the graphene sheet. In this dissertation, we focus on the effect of GBs on the tensile and thermal response of polycrystalline graphene. The fracture process of polycrystalline graphene sheets under uniaxial tension was studied using molecular dynamics (MD) simulations to determine how GBs affects the ultimate strength and critical failure strain of the graphene. We also study the flow of heat through polycrystalline graphene to determine the effect of GBs on the thermal conductivity of graphene. A comprehensive study including 24 GB misorientation angles ranging from 2.1° to 54.3° and the whole range of loading angle (i.e., that between a GB and in-plane tensile loading direction, ranging from 0° to 90°) was carried out to quantitatively determine the effect of GBs. Stress-strain data were generated from the MD simulations and the failure strength and critical strain were analyzed. A theoretical model combining continuum mechanics theory and disclination dipole theory was introduced to predict the failure strength of the polycrystalline graphene sheets, which was shown to be in good agreement with the MD simulation results. Various failure modes of polycrystalline graphene under tension were also analyzed. The thermal conductivity of polycrystalline graphene as a function of GB misorientation angle and thermal loading angle was also quantitatively determined through systematic simulations. The quantitative findings from this dissertation could potentially bridge the knowledge gap toward a better understanding of defects and their effects on two-dimensional materials, and also shed light on possible defect control and engineering to achieve desirable properties of graphene in applications.