The interaction of battery electrolytes with electrode surfaces is one of the key questions for the fundamental understanding of modern battery systems. Among others, it is decisive for the stability of the electrolyte and for the formation, stability and function of the solidelectrolyte interphase (SEI), which is indispensable as protective layer for the sustainable operation of modern battery systems. Initially, information about the build-up of the SEI and its performance came mainly from purely electrochemical measurements. While such measurements could provide detailed information on the performance of the SEI, insights about molecular aspects such as its molecular composition, the ongoing reactions and the transport processes determining their performance remained elusive. In recent years, these topics have been increasingly studied by a wide variety of spectroscopic and microscopic techniques, both in post-mortem analysis (ex situ) and in situ or even operando conditions, i.e., in the electrochemical environment or even under working conditions. Furthermore, theoretical studies, including both density functional theory (DFT) based calculations together with ab initio molecular dynamics (AIMD) simulations, and also continuum modelling provided increasing insights. The comparison between experimental and theoretical results often suffers, however, from the ill-defined structure and often also chemical composition of the electrode surface region in the experiments. In contrast, theoretical studies mostly deal with structurally well-defined, single-crystalline materials and model systems. Furthermore, also the theoretical description of the electrochemical environment is generally simplified.