Forty years after Ziegler's discovery of the "Aufbaureaktion" and low-pressure ethene polymerization, transition metal catalyzed olefin and diolefin polymerization continues to represent one of the most active and exciting areas. Since the 1980s, scientific innovations and process improvements have revolutionized polyolefin technology and greatly simplified polymerization processes. Well-defined catalyst systems are now at hand and facilitate the understanding of basic reaction mechanisms and correlations between catalyst structures, polymer microstructures, and polymer properties. This text reviews some of the modern approaches in organometallic chemistry, Ziegler-Natta catalysis, polymerization processes, the design of novel materials, and modelling in catalyst and process development.