This dissertation is composed of three chapters. Each chapter addresses a specific topic and has been, or will be, submitted as a journal article. The overarching theme connecting the content of the three chapters is the problem of accurately determining the rate off corrosion in alloy-electrolyte systems. At the beginning of every chapter there is a separate abstract that has been prepared for the respective journal publication. Broadly, in order to computationally simulate the process of corrosion we need the following: a knowledge of the physical laws that govern the rate of corrosion, a framework to compute the rate for alloy-electrolyte systems using these laws, and a method to update the position and the electrochemical properties of a corrosive front using the computed reaction rate. In the electrolytic domain, the effect of ionic concentration on the reaction rate is computed using ionic transport models. The most commonly used ionic transport model combines a set of Nernst-Planck equations with the electroneutrality condition without including the Gauss' law. On the other hand, the methods using Gauss' law have been reported to be challenging for a numerical solution. We developed an alternative ionic transport model based on Onsager's theory of nearequilibrium dissipative processes. We assumed the flow caused due to ionic interactions, as obtained using Onsager's theory, to be an additional unknown for the ionic transport model. We proposed that the flux density created due to this additional flow is the minimum that is required to satisfy the electroneutrality condition. Using our method we were able to reproduce the transient characteristics of electrodes that agreed in behavior with experimental observations. Also based on our numerical simulations, we observed that the dissipation due to ionic interactions is higher near the ionic sources at the boundaries and diminishes gradually into the bulk of the electrolyte. The motion of an alloy-electrolyte interface due to corrosion is a multiscale problem in time. The ionic transport process evolves at a time step depending on the diffusivity of the ions and dimensions of the anodic-cathodic regions on an alloy surface. It turns out that this time step is several order of magnitudes smaller than the time step at which we can observe a significant change in the alloy-electrolyte boundary due to corrosion. We proposed a quasi-steady state assumption in order to alleviate this problem. We assumed that for a fixed description of the alloy-electrolyte boundary there exists a steady state solution to the corrosion current density as dictated by the ionic transport process. This is a reasonable assumption for several corrosive systems, particularly for the ones surrounded by seawater. A finite element framework with adaptive remeshing was developed that uses the ionic transport model described above to determine the corrosion rate and explicitly integrate the motion of the corrosive front. We studied and observed the convergence of this method with respect to refinement in time steps. This framework was built to modify the electrodic properties along an alloy-electrolyte interface depending upon the material composition of the alloy domain. Using this methodology we can computationally determine the evolution of the anode-cathode ratio and the corrosion current density for given organization of anodic and cathodic phases within an alloy domain. Most of the alloy structures that suffer corrosion are designed to transfer mechanical load. Hence, it is important to understand the impact of a stress field on the reaction kinetics that has been experimentally measured for an unstressed alloy. We used a stress-dependent chemical potential from the Gibbs-Duhem equation and used it to derive the reaction kinetics along the lines of the wellestablished Butler-Volmer model. In the presence of a stress field our model introduces an additional amplification-reduction factor to the forward and the reverse components of the Butler-Volmer kinetics. We further explored that the mechanical-electrochemical coupling produces a change in the shape of a dissolution front in addition to the change in the reaction rate. In our study we also examined the possible change in the reaction rate due stress-induced surface instabilities. Our calculations show that the combined shift in the reaction rate due to stress and surface patterns can be quite different from the change obtained due to the same stress field in the absence of patterns.