When introducing theoretical models, we adopt a "hands-on" approach by providing substantial mathematical details and even computation codes in some cases. Prospects on remaining and emerging issues on impedance modelling of porous electrodes are presented. Afterwards, a wealth of impedance models developed for lithium-ion batteries and polymer electrolyte fuel cells are introduced. Readers can have a glimpse of the long history of porous electrode theory and in particular its impedance variants, acquaint themselves with the celebrated de Levie model and a general theoretical framework, retrace the journey of extending the de Levie model in three directions, namely, incorporating new physico-chemical processes, treating new structural effects, and considering high orders. This review focuses on physics-based models, as such models, compared to electrical circuit models, are more fundamental in our understanding of the porous electrodes, hence more reliable and more informative. Interpretation of EIS data needs model and fitting which largely determine the type and amount of information that could possibly be obtained, and thereby the efficacy of the EIS method. Electrochemical impedance spectroscopy (EIS) is widely used as a noninvasive, in situ characterization tool to investigate multi-phase (electronic, ionic, gaseous) transport and coupling interfacial reactions in porous electrodes. Porous electrodes are prevalent in electrochemical devices.
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