Recent advances in manufacturing technology, such as cyber–physical systems, industrial Internet, AI (Artificial Intelligence), and machine learning have driven the evolution of manufacturing architectures into integrated networks of automation devices, services, and enterprises. One of the resulting challenges of this evolution is the increased need for interoperability at different levels of the manufacturing ecosystem. The scope ranges from shop–floor software, devices, and control systems to Internet-based cloud-platforms, providing various services on-demand. Successful implementation of interoperability in smart manufacturing would, thus, result in effective communication and error-prone data-exchange between machines, sensors, actuators, users, systems, and platforms. A significant challenge to this is the architecture and the platforms that are used by machines and software packages. A better understanding of the subject can be achieved by studying industry-specific communication protocols and their respective logical semantics. A review of research conducted in this area is provided in this article to gain perspective on the various dimensions and types of interoperability. This article provides a multi-faceted approach to the research area of interoperability by reviewing key concepts and existing research efforts in the domain, as well as by discussing challenges and solutions.