In the following sections we want to explore todays most important material classes of crystalline solids, which are researched for their use in battery technology. Still, the aim of this review is not a full account on all material classes since unfortunately, covering all of them is far beyond the scope of this review. Therefore, we limited ourselves to the materials classes of spinels, olivines, Garnets, perovskites, Prussion blue, Chevrel phase, layered oxides, NASICONs and anion migration systems. We are aware of the plethora of other materials out there, such as post-spinels 87 , Weberites