In spite of the strong relevance of electrochemical energy conversion and storage, the atomistic modeling of structures and processes in electrochemical systems from first principles is hampered by severe problems. Among others, these problems are associated with the theoretical description of the electrode potential, the characterization of interfaces, the proper treatment of liquid electrolytes, changes in the bulk structure of battery electrodes, and limitations of the functionals used in first-principles electronic structure calculations. We will illustrate these obstacles, but also indicate strategies to overcome them. (C) 2014, Elsevier B.V. All rights reserved.