Magnesium-based rechargeable batteries might be an interesting future alternative to lithium-based batteries. It is so far well known that Mg2+ ion insertion into ion-transfer hosts proceeds slowly compared with Li+, so it is necessary to realize fast Mg2+ transport in the host in addition to other requirements as practical cathode materials for magnesium batteries. Positive electrode materials based on inorganic transition-metal oxides, sulfides, and borides are the only ones used up to now to insert magnesium ions. In this paper, the available results of research on materials suitable as possible, for secondary magnesium batteries, are reviewed.