Abstract: The invention pertains to the use of Group 8 transition metal carbene complexes as catalysts for olefin cross-metathesis reactions. In particular, ruthenium and osmium alkylidene complexes substituted with an N-heterocyclic carbene ligand are used to catalyze cross-metathesis reactions to provide a variety of substituted and functionalized olefins, including phosphonate-substituted olefins, directly halogenated olefins, 1,1,2-trisubstituted olefins, and quaternary allylic olefins. The invention further provides a method for creating functional diversity using the aforementioned complexes to catalyze cross-metathesis reactions of a first olefinic reactant, which may or may not be substituted with a functional group, with each of a plurality of different olefinic reactants, which may or may not be substituted with functional groups, to give a plurality of structurally distinct olefinic products.