During the 1950's the discoveries of Ziegler's organometallic catalyst systems and Natta's stereoselective olefin polymerization set the stage for extraordinary progress in polymer science and technology. Today advanced catalyst systems are available for catalytic carbon carbon bond formation by means of polyinsertion, metathesis, coupling reactions, and controlled radical polymerization. Modern catalytic olefin polymerization processes and polyolefins are environmentally friendly and meet the demands of a sustainable development. The architectures of homo‐ and copolymers based upon olefin, cycloolefin, diene, styrene and arene feed stocks are tailored as a function of single site catalysts' ligand frameworks. Polymer properties are varied over a very wide range, e.g., liquid/solid, rigid/soft, crystalline/amorphous/rubbery, permeable/impermeable, opaque/transparent, moldable/thermosetting, insulating/conducting. Advanced polymerization reaction engineering, copolymerization processes, reactor granule and reactor blend technologies, tailor‐made single site catalysts, catalyst blends and tandem catalysis improve property profiles, stability, morphology, and melt processing. Tuned cycloolefin polymers are new functional materials for electronic applications. Catalytic chain transfer (CCT) and atom transfer polymerization (ATRP) produce a variety of new functional polymers, reactive oligomers, and block copolymers. Aqueous polyolefin emulsions are obtained when catalytic olefin polymerization is performed in nanodroplets of catalyst miniemulsions. The scope of catalytic polymerization and post polymerization catalysis is progressing well beyond the frontiers of commodity polyolefin manufacturing. Advanced catalytic processes produce polar polymers such as polyethers, polyketones, polyesters, polycarbonates, polyamides, polyaramids, and polyimides. The new phosgene free polycarbonate syntheses are based upon the palladium catalyzed oxidative carbonylation. This overview highlights history, recent progress and modern trends in catalytic polymerization and catalytic polymer modification illustrated by selected examples.