  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}.
