In many phenomena at the electrode-electrolyte interface, electronic and atomic structure and dynamics are strongly interdependent in ways that challenge traditional theory and simulation techniques. We illustrate with some examples of our efforts to meet such challenges. In the case of the metal-aqueous electrolyte interface, we describe a recent direct dynamics model of the copper-water interface. For oxide-water interfaces, we review two methods : a self-consistent tight binding method applied to rutile surfaces and a polarizable, dissociable model of the water-ferric hydroxide interface. For modeling Faradaic reactions we describe recent progress on models of electron transfer reactions which shows that the rates are even more dependent on details of the electronic and atomic structure of the interface than traditional models might suggest.