Solid state Lithium-ion (Li-ion) batteries can revolutionize battery design and performance due to their inherent safety, high voltage stability, and potential for high conductivity. As the solid state Li-ion battery field grows, there is a need for simulation tools which allow battery engineers to explore the effects of material and geometry and their subsequent impact on performance, enabling optimization of a given battery design without expansive experimental tests. In this talk, we survey current research literature on modeling of solid state Li-ion batteries and discuss the challenges and opportunities that exist in developing a multi-physics modeling tool. A three-dimensional (3D) computational framework called AMPERES, developed at ORNL, is used as a case study to examine the requirements of modeling the electrode-electrolyte interface of solid state Li-ion batteries. Because AMPERES enables one to model arbitrary battery and electrode configurations, we also discuss potential 3D structures that can enhance mechanical stability and the effective conductivity of a solid state battery medium.