The discovery of the metallocene/methylaluminoxane catalysts for olefin, diene, and styrene polymerization has opened up a new millennium in the polymer science. Beside the classical Ziegler-Natta and Phillips systems, catalysts such as metallocenes, half-sandwich, nickel, palladium, and iron complexes have been synthesized-that give tailored polymers of totally different structures and allow to control the polymer tacticity, molar mass and molar mass distribution more efficient. New kinds of copolymers and elastomers can be synthesized. It has become possible to polymerize cyclic olefins with different zirconocenes or nickel and palladium catalysts without any ring opening reaction. The crystalline polycycloalkenes show extremely high melting points which are between 400 and 600 degreesC. Copolymers of cycloalkenes with ethene are amorphous and transparent with a glass transition temperature between 120 and 200 degreesC. The chemical industry is using these catalysts to produce increasing amounts of plastic material with special properties.