Currently, our understanding on how the atomic-scale properties of SCEs depend on the applied electrode potential, electrolyte, and electrode structure is far from complete and new theoretical and computational methods are needed to provide such understanding. In this article, we will focus on the first challenge; how to model the impact of an applied electrode potential in semiconductor electrochemistry using electronic structure methods. We have made a deliberate choice not to discuss the simulation of the electrolyte or out-of-equilibrium effects, such as light illumination or current. Within these restrictions, we are primarily interested in the merits and limitations of currently available computational approaches to model the applied electrode potential within density functional theory (DFT). Besides ground state DFT, we will briefly discuss the use of Green's function approach for describing the electrode potential.