This paper presents the evolution of alkyne metathesis since the early discoveries, essentially from the catalyst point of view. It is shown that although well defined carbynes may be useful for this reaction, further work has been made, aimed at the synthesis of new catalysts or catalytic systems, based on molybdenum precursors, associated or not with phenolic co-catalysts. The major objectives have been to obtain more functional groups tolerants catalysts, for their application in organic synthesis, including RCM for further stereoselective hydrogenation of the triple bond in the cycle, as well as for polymerization of aromatic diynes. Some insights into the possible mechanisms are given, and data relevant to the metathesis of terminal alkynes, a still challenging reaction where polymerization is occurring via the formation of deprotonated metallacyclobutadiene, are also presented and discussed. (c) 2006 Elsevier B.V. All rights reserved.