Transition-metal carbene complexes have been known for about 50years and widely applied as reagents and catalysts in organic transformations. In contrast, the carbene chemistry of the rare-earth metals is much less developed, but has attracted the research interest in the recent years. In this field rare-earth-metal alkylidene, especially methylidene, compounds are an emerging class of compounds with a high synthetic potential for organometallic chemistry and maybe in the future also for organic chemistry.