The phenomena stereoisomerism in the linear polymers of olefines and diolefines and the nature of the stereospecific polymerization processes are shortly discussed. They allowed the first synthesis of isotactic and syndiotactic polymers and of the four pure stereoisomers of polybutadiene, that is: the polymers having 1,2-isotactic, 1,2-syndiotactic, 1,4-cis, and 1,4-trans enchainments. The structure of catalytic complexes, that promove the stereospecific polymerization in the ionic coordinated catalysis, is pointed out. They are electron deficient complexes containing bridge-bonds between very electropositive transition metals, with valence less than the maximum, and very electropositive metals with very small ion diameter, to which electronegative carbon atoms are coordinated. Some soluble complexes, based on Titanium and Aluminum, are described, that act as catalysts in homogeneous solution. The best stereospecific catalysts for the synthesis of isotactic polymers are heterogeneous ones and their stereospecificity is connected with the presence of a crystalline substrate, formed by a layer lattice on which the active centers contain chemisorbed or epitattely bound metallorganic complexes (that may exist in enantiomorphous forms).