In this paper, we introduce cloud supply chain which is a business model based on cloud-enabled networking of some third-party physical and digital assets to design and manage a supply chain network. Cloud supply chain integrates concepts and technology of Industry 4.0 and digital platforms emerging in the “supply chain-as-a-service” paradigm. This paper conceptualizes the cloud supply chain as a new and distinct research area. Through analysis of practical cases, we deduce some generalized characteristics of the cloud supply chain. In the generalised model, we formalize supply chain multi-structural dynamics and dynamic service composition. Our results show that the main generalized characteristics of the cloud supply chain are related to (i) multi-structural dynamics; (ii) platforms, digital supply chains, ecosystems, and visibility, (iii) dynamic service composition with dynamically changing buyer/supplier roles, (iv) resilience and viability, and (v) intertwined supply networks and circular economy. We close by discussing future research directions including novel context of Industry 5.0.