In recent times, there has been significant enthusiasm for the development of all solid state batteries. This interest stems from a dual focus on safety—addressing concerns related to toxic and flammable organic liquid electrolytes—and the pursuit of high energy density. \cite{SCHNELL2018160,Zheng2018}. While liquid electrolyte batteries constitute for now the vast majority of commercial cells, solid electrolyte batteries show great promise.
In parallel with experimental research, computational models \cite{GrazioliEtAlCM2016} clarify the several fundamental physics \cite{LiMonroeARCBM2020} that take place throughout battery operations.
We review some classical models, emphasizing the conceptual advancements documented in the most recent works.