Metallocenes in combination with methylalumoxane as cocatalyst form extremely active catalysts for olefin polymerization and have become a research topic of growing interest in recent years. Meanwhile a great number of symmetric and chiral zirconocenes have been synthesized to give totally different structures of isotactic syndiotactic, stereoblock, or isoblock polymers. The isotactic sequence length of polypropylene is influenced by the nature of the ligands of the metallocenes. It has become possible to polymerize cyclic olefins like cyclopentene, norbornene, or dimethanooctahydronaphthalene with different chiral zirconocenes without any ring opening reaction. The crystalline polycycloalkenes show extremely high melting points which are between 400 and 600-degrees-C. Copolymers of cyclo-alkenes with ethene are amorphous and transparent with a glass transition temperature between 120 and 160-degrees-C and they can be used as materials for optical discs and fibers.