Nanostructures are emerging as novel materials with revolutionary application in electronics, nuclear reactors, structures, aerospace, and energy. Nanocrystalline structures owe their outstanding mechanical properties to their nanoscale grain size and high density of crystalline interfaces called grain boundaries. Recently, nanotwinned structures, containing special grain boundaries called twin boundaries, have become quite attractive as optimal motifs for strength, ductility, and grain stability in metals. This dissertation presents our atomistic study of the role of these grain boundaries and twin boundaries in governing the mechanical response of nanostructures by way of different atomistic simulation methods. Nanopillar compression is first used to investigate the interplay between size effects associated with the twin spacing and the finite size of nanopillars by molecular dynamics. Simulations reveal that there exists an optimal aspect ratio for which the yield strength of twinned nanopillars is higher than even single crystal nanopillars. In addition, it is observed that twin boundaries facilitate dislocation-starvation as defects glide along twin boundaries and are annihilated at the free surface. Approaching experimentally-relevant strain rates has been a long-standing bottleneck for molecular dynamics. In this study, shearing of a nanopillar with a grain boundary is used as a paradigmatic problem to investigate the rate dependence of grain boundary sliding in nanostructures. A combination of time-scaling approaches is used including the recently developed autonomous basin climbing method, the nudged elastic band method, and kinetic Monte Carlo, to access strain rates ranging from 0.5s-1 to 107s-1. Although grain boundary sliding is the primary mechanism observed in all simulations, at lower strain rate, sliding initiates at significantly lower stress and occurs on the time-scale of seconds which is beyond the reach of conventional molecular dynamics. Finally the time scaling approach is used to investigate the diffusion of radiation-induced point defects through nanotwinned metals. The simulations reveal that dumbbell interstitials can cross coherent twin boundaries in three low energy barrier steps which can occur even at room temperature. Furthermore, the method shows that Frenkel pairs have greater probability to recombine in the vicinity of coherent twin boundaries which is consistent with observations reported by other computational studies.