The treatise supports understanding the phenomena of complexity in engineering, distinguishes complexity from other challenges and presents an overview of definitions and applied approaches.The historical background of complexity management is explained by highlighting the important epochs, their key actors and their discoveries, findings and developments. Knowing about the appearance of early system awareness in ancient Greece, the creation of mechanical philosophy in the 17th century and the discovery of classic physics enables the reader to better comprehend modern system sciences and management approaches.A classification of complexity management approaches by research fields indicates current focus areas and starting points for future discussions. In a comprehensive map, the classification points out mutual overlaps between engineering disciplines in terms of similar complexity management approaches.Finally, the treatise introduces a generic complexity management framework, which is based on structural management approaches.