Several systems consisting of a ligand, a metal compound, and zinc have been developed as catalysts for alkyne cycloaddition reactions and alkyne-nitrile co-cycloaddition reactions. N-Heterocyclic carbene (NHC)-iron(III) chloride-zinc, NHC-cobalt(II) chloride-zinc, and 2-{ [(2,6-diisopropylphenyl)imino]meth-yl}pyridine (dipimp)-iron(III) chloride hexahydrate-zinc systems catalyzed intramolecular cyclotrimerization reactions of alkynes. The dipimp-cobalt(II) chloride hexahydrate-zinc system catalyzed cycloaddition reactions of a variety of alkynes in intramolecular, partially intramolecular, and fully intermolecular fashions. The ethane-1,2-diylbis(diphenylphosphine)-cobalt(II) chloride hexahydrate-zinc system was effective in catalyzing the [2 + 2 + 2] cocycloaddition of diynes with nitriles. Nickel complexes with an ionic liquid-tagged ligand converted 1,6-diynes into the corresponding cyclooctatetraenes in a toluene-ionic liquid biphasic system in the presence of zinc. The dipimp-nickel(II) chloride hexahydrate-zinc catalyst polymerized 1,6-diynes to form conjugated polyene cyclic polymers. These results and their applications in synthesis, including controlled polymerization reactions, are described. 1 Introduction 2 Alkyne [2+2+2] Cycloaddition 2.1 Development of N-Heterocyclic Carbene-Cobalt or Iron Compound-Zinc Catalyst Systems 2.2 Development of 2-{[(2,6-Diisopropylphenyl)imino]meth-yl}pyridine-Cobalt or Iron Salt-Zinc Catalyst Systems 2.2.1 Development of 2-{[(2,6-Diisopropylphenyl)imino]meth-yl}pyridine-Iron Chloride-Zinc Catalyst Systems 2.2.2 Development of the 2-{[(2,6-Diisopropylphenyl)imino]methyl}pyridine-Iron Chloride Hexahydrate-Zinc Catalyst System 2.3 The 2-{[(2,6-Diisopropylphenyl)imino]methyl}pyridine-Cobalt(II) Chloride Hexahydrate-Zinc Catalyst System 2.3.