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 is an emerging but conceptually different construct than CPS. Like CPS, DT relies on communication to create a highly-consistent, synchronized digital mirror image of the objects or physical processes. DT, in addition, uses built-in models on this precise image to simulate, analyze, predict, and optimize their real-time operation using feedback. DT is rapidly diffusing in the industries with recent 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 in next-generation (NextG) wireless technologies (e.g., 5G and beyond networks), various tools (e.g., age of information, federated learning, data analytics), and other promising trends in networked computing (e.g., edge and cloud computing). Moreover, we discuss the DT deployment strategies at different industrial 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 DTs adoption.