The topotactic insertion/extraction of lithium in layered oxides and sulfides is compared with that in the oxo- and thiospinel frameworks [M2]X4 for both the technical interest of tailoring secondary-battery cathode materials and the scientific interest of exploring narrow-band phenomena and magnetic interactions in compounds and/or phases not accessible by conventional high-temperature techniques. It is pointed out that in layered LiyCoO 2 the higher voltages accessible in oxides is compatible with the higher Li+ -ion mobilities needed in power cells, but that fast three-dimensional Li+ -ion conduction in oxides requires a framework structure such as the monoclinic/orthorhombic Fe2(MO4)3 structure stabilized by M = Mo, W, and S. The influence of the counter cation on the working redox potential is illustrated by a 0.6 eV shift in the Fe3+/2+ redox couple on going from M = Mo or W to M = S.