Since Schrock and Grubbs discovered the molybdenum and ruthenium-carbene complexes in 1990 and 1992, metathesis reactions have been a useful tool in synthetic organic chemistry. As the metathesis reaction, olefin metathesis, enyne metathesis and alkyne metathesis are known. The carbon-carbon double or triple bonds are cleaved and the double or triple bonds are formed simultaneously in the metathesis reaction. Novel synthetic methods for the carbo- and hetero-cyclic compounds from diene, enyne and diyne have been developed using these reactions. The tandem metathesis reactions were also developed and many bond cleavages and bond formations occurred in one step reaction to form various functionalized compounds. For development of asymmetric metathesis reaction, novel molybdenum- and ruthenium-catalysts were also synthesized and asymmetric ring-opening and ring-closing metatheses were carried out to form optically active compounds with the high ee. The novel syntheses of the natural products and the biologically active substances have been achieved using these reactions.