The way of dealing with the strongly increasing complexity of the company itself and its environment has become a key competitive factor. Complexity factors in a variety of different business areas require an advanced Complexity Management. Therefore, knowledge regarding the specifics of the respective complexity, the so-called Complexity Footprint, is decisive to meet requirements and to derive measures by using appropriate instruments. The current Fraunhofer IPA empirical study "advanced Complexity Management -the new management discipline" with more than 190 industrial participants shows, that companies expect a future increase in complexity, but not yet have the tools to deal with it. Furthermore, complexity management is mostly focused on the complexity field product and here in product modularization and variety management. The importance of ideal complexity, of product profitability in response to product complexity in connection with complexity in process and organization is mostly ignored.Within this paper the different activities and instruments of advanced Complexity Management are presented. This includes the approach of complexity patterns in value networks including production and supply chain as well as the summary of several complexity patterns to the Fraunhofer IPA Complexity Footprint. First an up-to-date survey on complexity in value networks is given. Then, the Stuttgart complexity comprehension is introduced. To define the external and internal complexity in socio-technical systems like value networks, the differences are presented. The difference between complicacy and complexity is given, within the complexity dimensions variety, heterogeneity, dynamics and opacity. After this, complexity fields such as goods and services, process and organization as well as their several subfields connectivity and interdependency are established. Examples for complexity in each field are given to highlight the different appearance of complexity. Following, the advanced Complexity Management is introduced and finally the Fraunhofer IPA Complexity Footprint is introduced. Within this Complexity Footprint the complexity patterns in value networks are located and a description is given.