In recent years, digital twins have been pervading different application domains – from manufacturing to healthcare - as a reference approach for virtualising the physical world (things, products, machines, people, processes), based on the development and widespread diffusion of Internet of Things technologies and architectures. Actually, the dominant view developed in literature so far is about the virtualisation of individual physical assets, in a closed-system perspective. In this paper we introduce and explore a broader perspective that we call the Web of Digital Twins (WoDT), in which the digital twin paradigm is exploited for the pervasive digitisation of possibly large-scale interrelated physical realities, resulting in open ecosystems of connected digital twins. In this view, agents and multiagent systems are adopted as a main reference for designing intelligent autonomous systems on top of aWoDT. To support agent reasoning and the development of smart, situated, cross-domain applications, the semantic model of a WoDT is based on knowledge graphs.