We discuss some of the limitations of conventional density-functional calculations in describing electrochemical interfaces. First, we analyze orbital-overhybridization errors in predicting the energetic, structural and vibrational properties of molecular adsorbates on catalytic surfaces. We consider in particular the adsorption of carbon monoxide on fuel-cell electrodes. Second, we discuss the electrostatics of charged surfaces in periodic-boundary conditions and propose an efficient computational approach to eliminate periodic-image errors in such systems. Finally, we present a first-principles method extending the applicability of conventional density-functional approaches to the description of electrochemical surfaces in the constant-potential regime. As an application, we study the influence of the electrode potential on the vibrational properties of carbon monoxide adsorbed on platinum-ruthenium electrodes.