This chapter introduces candidates for insertion electrodes for rechargeable Mg batteries with two representative mechanisms, namely (1) intercalation into layered materials and (2) conversion or displacement. In particular, the intercalation of Mg²⁺ into layered materials has been at the center of research interests and much controversy at the same time. This chapter summarizes and discusses the on-going history of research and recent debates on the issues based on the authors' experiences and perspectives. In addition, the later part of this chapter describes new avenues for cathode materials based on conversion or displacement reactions. These contents will equip the readers with clearer perspectives on this controversial yet pivotal issue of developing genuine insertion electrodes for magnesium batteries.