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For molecular engineering of polymers,precision control of polymerization is of course critical and indispensable.In these recent decades,we have been developing two "precision polymerizations": Lewis acid-catalyzed cationic living polymerization and transition metal-catalyzed living radical polymerization (Fig.1).This Plenary Lecture will discuss most updated advances in the precision synthesis of functional polymers therein (Fig.2).The target polymers include: (a) precision random copolymers of controlled molecular weight and compositional uniformity;(b) single-chain folding amphiphilic polymers from (a);core-functionalized star polymers for molecular recognition and catalysis;(d) sequence-controlled macromolecules toward autonomous function and information storage.