The subject of this work is the development of accurate frameworks to describe the electrochemical promotion of catalysis (EPOC) phenomenon. EPOC, also known as non-Faradaic electrochemical modification of catalytic activity (NEMCA), refers to the enhancement of the catalytic performance by application of current or potential in a catalyst/support system. Although this technology is of increasing interest nowadays in the field of modern electrochemistry and exhibits a great industrial potential, there are still just a few commercial applications, partly because the addressed phenomenon is not fully understood and has not been modelled to allow robust system design and control. For this purpose, a systematic multi-dimensional, isothermal, dynamic model is developed to address the EPOC phenomenon using the electrochemical oxidation of CO over Pt/YSZ as an illustrative system. The formulated model is based on partial differential equations (PDEs) accounting for the simulation of the mass and charge transport as well as the electrochemical phenomena taking place at the triple phase boundaries (TPBs, where the gas phase, the catalyst and the support are all in contact) implemented through a commercial finite element method (FEM) software (COMSOL Multiphysics). The constructed model is used in conjunction with experimental data for parameter estimation purposes, and a validated model is obtained. The results demonstrate that the effect in such a system is strongly non-Faradaic, with Faradaic rates 3 orders of magnidute lower than the non-Faradaic ones. The formulated model is extended to describe the various processes taking place in the electrochemically promoted CO combustion system at their characteristic length-scales. The proposed framework couples a macroscopic model simulating charge transport as well as electrochemical phenomena occuring at the TPBs implemented through a FEM-package and an in-house developed efficient implementation of the kinetic Monte Carlo method (kMC) for the simulation of reaction-diffusion micro-processes on the catalyst. Dynamic communication of macro- and micro-scopic models at the TPBs results in the construction of an integrated multi-scale system. Comparison between the multi-scale framework and a fully macroscopic model is carried out for several sets of operating conditions and differences between the two models steady-state outputs are presented and discussed. A detailed FEM/kMC model, regardless of accurately simulating the several phenomena at their appropriate length-scales, might not be suitable for large system simulations due to the high computational demand. To address this limitation, a computationally efficient coarse-graining methodology, the so-called gap-tooth method, is implemented. In this scheme the catalytic surface is efficiently represented by a small subset of the spatial domain (tooth) separated by gaps. While kMC simulations within each individual tooth (micro-lattice) are used to predict the corresponding evolution of the micro-processes, intelligent interpolation rules are employed to allow for the exchange (diffusion) of species between consecutive micro-lattices. A validated gap-tooth/kMC scheme is obtained and it is exploited for FEM/gap-tooth/kMC electrochemically promoted CO oxidation simulations achieving high computational savings.