Work in the field of application of metallocene-based catalysis in olefin, diolefin and styrene polymerization has become a research topic of growing interest in recent years. A great number of symmetric and chiral zirconocenes have been synthesized, that give tailored polymers of totally different structures. Single site catalysts have the capability of permitting the user to control polymer tacticity, molecular weight and molecular weight distribution more efficiently. Beside the homopolymers of polyethylene and poly(propylene), new kinds of copolymers and elastomers can be synthesized.