After addressing various atomistic models of SCEs, we discussed different electronic structure methods for simulating SCEs as a function of the electrode potential. It was emphasised that while the computational hydrogen electrode method is simple to use, it cannot describe for instance the impact of potential-dependent defect, surface, or polaron states or the SCR. While electrostatic or capacitance corrections on canonical DFT are in principle exact ways of including the electrode potential effects, their usefulness is limited by the lack of accurate semiconductor capacitance models or experimental data. In particular, the capacitance corrections should account for the presence of defect/surface/polaronic states and the SCR (see Figure ) and it is not enough to have a good model of the electrolyte capacitance because the semiconductor capacitance often dominates the total capacitance. Data on well-defined test systems is needed to make capacitance corrections useful and capacitance data on single crystal SCEs at different dopant concentrations would be particularly valuable. We also pointed out that in addition to interpolating to infinite surface sizes in metallic systems, SCEs require interpolation to infinite simulation cell thicknesses as well and this interpolation is expected to converge slowly due to the extended SCR.. In discussing GC-DFT simulations of SCEs as an explicit function of the electrode potential, we highlighted that very thick slab models are to achieve fully converged calculations and highlighted the utility of the recent CIP-DFT approach. We also reviewed the use of DFT with Green function theory for simulating SCE in a semi-infinite surface setup and emphasized that this is the only model that enables genuine control over the electrode (bulk) Fermi level.