Editorial Overview: Fundamental and Theoretical Electrochemistry Advances in the theory of electrochemical interfaces Martin Z. Bazant Electrochemical systems consist of electrolytes in contact with electrodes and other bounding surfaces. These bulk components are straightforward to characterize experimentally, and predictive theories and molecular simulations are also available. The interfaces, however, are much more challenging to understand and describe quantitatively. Interfaces play the primary role in charge storage (capacitance), reaction rates (resistance), and electrokinetic phenomena (motion) in electro- chemical systems, yet they continue to be modeled by simple equations that have hardly changed over the past century. Textbook examples include the ButlereVolmer (BV) equation for Faradaic reaction kinetics [1,2], the FrumkineTemkin isotherm for ion adsorption [2], the Poissone Boltzmann (PB) equation for electric double layer structure [3], the NernstePlanck equations for ion transport [1], the HelmholtzeSmolu- chowski slip formula for electroosmosis [1,3], and the Randles circuit for interfacial impedance [4]. In many models, interfacial structure is neglected altogether and empirical circuit elements are used, effectively as a ‘black box’, with parameters fitted to experimental data. One might expect the situation to have improved during the Computer Age. Indeed, many insights have come from ab initio quantum simulations, molecular dynamics, multiscale modeling, and machine learning, but many factors d disorder, chemical heterogeneity, multistep reactions, mixed ioneelectron transfer, long-range Coulomb forces, and specific in- teractions d render first-principles modeling almost impossible, except for simple model systems. Unfortunately, the experimental characteriza- tion of real interfaces is even more difficult, at all the relevant length and time scales. As a result, engineering models have not evolved as quickly as the ability to solve them on a computer. Over the past decade, there has been an explosion of interest in extending the classical equations of electrochemistry to situations far beyond their range of validity. As a sign of the coming ‘paradigm shift’, the same nonmonotonic double-layer capacitance formula was independently published only a few weeks apart in 2007, by Kornyshev [5] for room- Current Opinion in Electrochemistry 2019, 13:A1 – A4 This review comes from a themed issue on Fundamental and Theoretical Electrochemistry Edited by Martin Z. Bazant https://doi.org/10.1016/j.coelec.2019.02.008 2451-9103/© 2019 Published by Elsevier B.V. Martin Z. Bazant Martin Z. Bazant is the E. G. Roos (1944) Professor of Chemical Engineering and Mathematics at the Massachusetts Institute of Technology, executive officer of the Depart- ment of Chemical Engineering, Fellow of the ISE, RSC, and APS, and winner of the Alex- ander Kuznetsov Prize in Theoretical Electrochemistry. Available online at www.sciencedirect.com ScienceDirect Current Opinion in Electrochemistry www.sciencedirect.com Current Opinion in Electrochemistry 2019, 13:A1 – A4