By amalgamating recent communication and control technologies, computing and data analytics techniques, and modular manufacturing, Industry 4.0 promotes integrating cyber–physical worlds through cyber–physical systems (CPS) and digital twin (DT) for monitoring, optimization, and prognostics of industrial processes. A DT enables interaction with the digital image of the industrial physical objects/processes to simulate, analyze, and control their real-time operation. DT is rapidly diffusing in numerous industries with the interdisciplinary advances in the industrial Internet of things (IIoT), edge and cloud computing, machine learning, artificial intelligence, and advanced data analytics. However, the existing literature lacks in identifying and discussing the role and requirements of these technologies in DT-enabled industries from the communication and computing perspective. In this article, we first present the functional aspects, appeal, and innovative use of DT in smart industries. Then, we elaborate on this perspective by systematically reviewing and reflecting on recent research trends in next-generation (NextG) wireless technologies (e.g., 5G-and-Beyond networks) and design tools, and current computational intelligence paradigms (e.g., edge and cloud computing-enabled data analytics, federated learning). Moreover, we discuss the DT deployment strategies at different communication layers to meet the monitoring and control requirements of industrial applications. We also outline several key reflections and future research challenges and directions to facilitate industrial DT's adoption. © 2021 The Author(s)