We tackle the problem of digitalisation of Supply Chains, focusing on collaboration and sharing of information. By generalising the notion of Digital Twins, we review, develop, and conceptualise the (emerging) notion of Digital Twins of Supply Chains (DTofSC). Whereas Digital Twins is an active research area with data available from numerous industry projects, its application to Supply Chains is just emerging as a cross-discipline stemming from decades of maturing the notion of Digital Supply Chains. Whereas Digital Twins has been used in Supply Chains, the notion of digitalisation of Supply Chains is only a nascent area, with imprecise definition beyond key metaphors (e.g., visibility, traceability); as we conceptualise, the overall vision is to create technical and organisational mechanisms enabling any Supply Chain to be monitored and controlled from, e.g., a dashboard screen. After a literature review on the intersections between Digital Supply Chains, Digital Twins, and digital technologies (e.g. Blockchain), we (1) propose a synthesis systems architecture of DTofSC, (2) identify a key requirement gap (that we term addressability), and (3) to ground our contributions and in the absence of real-world use-cases in practice, we apply our conceptualised systems architecture to battery recycling based on feedback from an industry-targeted workshop.