Digital twins involve the integration of advanced information technologies to create software replicas that control and monitor physical assets. Interoperability is an essential requirement in the engineering of digital twins. This paper is the first study analysing interoperability in digital twin software architectures in the manufacturing industry. We began with an initial set of 2403 peer-reviewed publications and after a screening process, we selected a final set of 21 primary studies. We identified the set of technologies used for data exchange and the level of interoperability achieved during such an exchange. We organised the results according to the ISO 23247 standard and the level of conceptual interoperability model.