Topics in "Number 36" include: Electrochemical nuclear magnetic resonance (EC-NMR). This powerful non-invasive technique brings new insights to both fundamental and practical key aspects of electrocatalysis, including the design of better anodes for PEM fuel cells; The recent impressive advances in the use of rigorous ab initio quantum chemical calculations in electrochemistry. This lucid chapter is addressed to all electrochemists, including those with very little prior exposure to quantum chemistry, and demonstrates the usefulness of ab initio calculations, including density functional theory (DFT) methods, to understand several key aspects of fuel cell electrocatalysis at the molecular level; The most important macroscopic and statistical thermodynamic models developed to describe adsorption phenomena on electrodes, including the current state of the art adsorption isotherms, which are both rigorous, and in good agreement with experiment.It also includes: Electrochemical promotion i.e., the use of electrochemistry to activate and in situ tune the catalytic activity and selectivity of metal and metal oxide catalysts interfaced with solid electrolytes; and Lithium transport through transition metal oxides and carbonaceous materials, which is of paramount importance in rechargeable lithium batteries.