Supply chain agility and resilience are key factors for the success of manufacturing companies in their attempt to respond to dynamic changes. The circular economy, the need for optimized material flows, ad-hoc responses and personalization are some of the trends that require supply chains to become "cognitive", i.e., able to predict trends and flexible enough in dynamic environments, ensuring optimized operational performance. Digital twins (DTs) is a promising technology, and a lot of work is done on the factory level. In this paper, the concept of cognitive digital twins (CDTs) and how they can be deployed in connected and agile supply chains is elaborated. The need for CDTs in the supply chain as well as the main CDT enablers and how they can be deployed under an operational model in agile networks is described. More emphasis is given on the modelling, cognition and governance aspects as well as on how a supply chain can be configured as a network of connected CDTs. Finally, a deployment methodology of the developed model into an example of a circular supply chain is proposed.