Olefin polymers (such as polypropylene and polyethylene) have seen widespread use in the plastics industry in the past 50 years.  A way to enhance the properties of these olefin polymers was first discovered by the scientists Karl Ziegler and Giulio Natta.  Ziegler discovered the original Titanium based catalyst essential for olefin polymerization, while Natta used the catalyst to alter and control the stereochemistry (tacticity) of the olefin polymers (hence Ziegler–Natta catalyst).  By controlling the tacticity of the polymer, a chain can, for example, either be semi crystalline or amorphous, rigid or elastic, heat resistant or have a low glass transition temperature.  Much research since has been dedicated to predicting and creating polymers based on this work.  Living polymerization is the term coined to describe the use of specially made catalysts (often involving transition metal centers) in olefin polymerization, since the polymer chains self-propagate in the presence of the catalyst until intentionally terminated.
Living polymerization, however, produces only one type of tacticity per catalyst.  While the specific tacticity can be controlled by altering the type of catalyst used, creating a block copolymer requires that the polymerization be terminated, the catalyst destroyed, and that the chain re-propagate using another catalyst that produces the desired stereochemistry.  Such manipulations are usually difficult, however.