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This thesis summarizes a study of the effects of electromigration on nanoscale metallic structures. We have studied the impact of electromigration on two types of nanoscale systems, and as such the thesis naturally divides into two portions. In the first portion, consisting of Chapters 2-4, we investigate the effects of electromigration on fluctuating step edges. When there is no electromigration present, a step undergoing motion by atoms diffusing along its edge demonstrates power-law scaling in temporal correlation functions. This is verified by approximating the step as a continuum and using Langevin analysis, and the Langevin analysis is extended to include electromigration forces. Under electromigration conditions, specifically for electromigration forces directed into or out-of the step, we find theoretical deviations from the power-law scaling in the correlation function. We demonstrate this in two ways: through Monte Carlo simulation of step edges under electromigration conditions and through experimental measurements of current-stressed steps at the surface of Silver films. We found good phenomenological agreement with the theoretical expectations in both simulation and experiment, as well as good quantitative agreement in the results of the simulations. The second portion of the thesis, consisting of Chapters 5 and 6, detail an investigation of the effects of electromigration on the Rayleigh-Plateau instability in solid nanowires. We begin by deriving an equation of motion for a continuous cylinder and including an electromigration force along the symmetry axis of the cylinder. This is equivalent to a model of a nanowire carrying current, where the electromigration force is modeled as a constant. We find power-law scaling in the pinching process, though the effects of electromigration are to extend the life of the nanowire by prolonging the pinch-off. This is confirmed by conducting kinetic Monte Carlo simulations of Aluminum nanowires under electromigration conditions. We find good agreement with the continuum model for the exponent in the power-law scaling as well as the effect of electromigration on the time at which pinching occurs. We find evidence of self-similar behavior in the continuum model as well as in the simulations.

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