Latent and thermochemical heat storage technologies are receiving increased attention due to their important role in addressing the challenges of variable renewable energy generation and waste heat availability, as well as the mismatch between energy supply and demand in time and space. However, as the operating storage temperature increases, a series of challenging technical problems arise, such as complex heat transfer mechanisms, increased corrosion, material failure, reduced strength, and high-temperature measurement difficulties, especially for metals and metallic compounds as heat storage media. This paper reviews the latest research progress in medium- and high-temperature latent and thermochemical heat storage using metals and metallic compounds as storage media from a technical perspective and provides useful information for researchers and engineers in the field of energy storage. In this paper, the status and challenges of medium- and high-temperature latent and thermochemical heat storage are first introduced, followed by an assessment of metals and metallic compounds as heat storage media in latent and thermochemical heat storage applications. This is followed by a comprehensive review of three key issues associated with medium/high-temperature latent heat storage applications: heat transfer enhancement, stability and corrosion, as well as a discussion of four key issues associated with medium/high-temperature thermochemical heat storage: heat transfer, cycling stability, mechanical property and reactor/system design. Finally, the prospects of medium/high-temperature latent and thermochemical heat storage are summarized.