The mechanical properties of polycrystalline materials are governed by the underlying microstructure. In this context, in this dissertation, the role of grain boundaries on the mechanical response of two technologically important materials namely silicon and silicon carbide are examined. In particular, the dynamics of silicon carbide and silicon symmetric tilt bicrystals under shear load are characterized via molecular dynamics simulations. Cubic silicon carbide bicrystals with low-angle grain boundaries exhibit stick-slip behavior due to athermal climb of edge dislocations along the grain boundary at low temperatures. With increasing temperature, stick-slip becomes less pronounced due to competing dislocation glide, and at high-temperatures, structural disordering of the low-angle grain boundary inhibits stick-slip. In contrast, structural disordering of the high-angle grain boundary is induced under shear even at low temperatures, resulting in a significantly dampened stick-slip behavior. When a single layer graphene sheet is introduced at the grain boundary of the symmetric tilt silicon-carbide bicrystals, the resultant shear response is dictated by the orientation of the graphene sheet. Specifically, when the graphene layer is oriented perpendicular to the gain boundary, stick-slip behavior displayed by the low-angle grain boundaries is inhibited, though both low-angle and high-angle grain boundaries exhibit displacement along crystallographic planes parallel with the applied shear direction. On the other hand, when the graphene sheet is parallel to the grain boundary, shear deformation at the grain boundary for both low-angle and high-angle bicrystals is diminished. In silicon bicrystals, high-angle grain boundaries demonstrate coupled motion, characterized by an additional normal motion of the grain boundary. Interestingly, this phenomenon was observed previously in metallic materials. Further, the grain boundary coupling factor, which is ratio of the grain boundary normal velocity to the grain translation velocity, matches the predicted geometric value. The underlying atomic scale mechanisms that govern the grain boundary coupled motion consists of concerted rotations of silicon tetrahedra within the grain boundary. For low-angle grain boundaries in silicon, the activation of dislocation glide along the predicted slip-plane takes precedence and no grain boundary coupling is observed. This behavior is similar to that of silicon carbide seen at high-temperatures but for silicon it occurs for a large temperature window.