What is Olefin metathesis?

Olefin metathesis is the exchange of the alkylidene halves of two alkenes, $\mathrm{RCH{=}CHR + R'CH{=}CHR' \rightleftharpoons 2\,RCH{=}CHR'}$, catalysed by metal carbene complexes through a metallacyclobutane, a four-membered ring of the metal and three carbons. Its synthetic forms are ring-closing metathesis (RCM), which joins two alkene ends of one molecule into a ring with loss of ethene, ring-opening metathesis polymerisation (ROMP) of strained cyclic alkenes, and cross metathesis between two different alkenes.