Complexity is regarded a major impediment to Supply Chain (SC) performance. However, very few studies aid SC managers adopt adequate practices in response to structural and dynamic complexity. This study offers a comprehensive review of the practices that four manufacturing companies employ in their SC function to manage the structural and dynamic complexity of their product portfolio, internal SC, and supplier and customer bases. Moreover, leveraging the results of the inductive in-depth case studies, a classification of complexity management practices consisting of four clusters is advanced: variety reducing, confinement and decoupling, coordination and collaboration and decision support and knowledge generation. Each cluster's distinctive logic and limitations are discussed and propositions on their managerial scope are introduced, therefore providing managers with relevant insights to design effective complexity management approaches in their organisations.