There is a wide class of different crystalline materials used in batteries such as spinels, perovskites, olivines, Prussion blue, NASICON, Chevrel phase, layered oxides, and van der Waals bonded layered systems. Apart from the structural differences of all these material classes, the interaction of the migrating ion with these different host lattices differs to a certain extent as well. Hence we will dedicate a full section to each of these materials classes.