The term “carbene” is applied to organic compounds described as CR₂. A transition metal complex having this as a ligand is referred to as a “carbene complex”, and may be written MCR₂ with a double bond between M and C. There is a large difference in stability and reactivity between complexes with and without heteroatoms (such as N, O, and S atoms) on the carbene carbon. They are thus frequently distinguished by referring to the former as Fischer carbene complexes and to the latter as Schrock carbene complexes, named for the chemists who first synthesized them. This chapter describes the features and reactivity of carbene complexes.