In recent years there has been a major interest in developing all solid state batteries, for the sake of safety (issues due to toxic and flammable organic liquid electrolytes are well known) as well as of high energy density \cite{SCHNELL2018160,Zheng2018}. Side by side to experimental investigations, computational simulations \cite{GrazioliEtAlCM2016} unveil the several physics that interconnect at different scales \cite{LiMonroeARCBM2020} during battery operations. %Several advanced mathematical models have therefore been published \cite{bistriM2020}. We propose herein a new advanced model, which is multiscale compatible and fully three dimensional in nature. Furthermore, we review some classical or inspiring models, highlighting the conceptual evolutions that are ultimately collected in our work. The model is validated against experimental evidences of a Li/LiPON/LiCoO$_2$ thin film battery published in \cite{Danilovetal2011}.