What is Carbenes and carbene complexes?

A carbene is a neutral species $\ce{R2C}$ with a divalent carbon carrying two non-bonding electrons. A carbene complex has a $\ce{CR2}$ ligand bonded to a metal by a double bond, $\ce{M=CR2}$. A Fischer carbene complex has a heteroatom substituent on the carbene carbon and a low-valent metal with $\pi$-acceptor ligands; its carbene carbon is electrophilic. A Schrock carbene (alkylidene) complex has only C or H substituents and a high-valent early metal; its carbon is nucleophilic. An N-heterocyclic carbene is a cyclic carbene flanked by two nitrogen atoms, stable as a free compound and a strong $\sigma$-donor ligand.