This book addresses the topic of modeling and numerical simulation of electrochemical devices type batteries and supercapacitors through various theoretical approaches, each aiming a description of physico-chemical phenomena occurring at different temporal and spatial scales. The application of these methods to the analysis of experimental characterization and interpretation of redox and transport mechanisms occurring in current electrochemical devices is illustrated with concrete examples in each Section. Special attention is given to the application of some of these approaches to the simulation of manufacturing composite electrodes and the technical multiscale modeling which allow, as their name suggests, to take into account within the same formalism of events occurring at different scales. These emerging methods aim to translate the microscopic properties of the various elements used in electrochemical devices at the macroscopic behavior of the whole cell in operating conditions. All the available methods and methodological bolts remaining to be exercised are also discussed.