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Industrial Internet of Things is an ultra-large-scale system that is much more sophisticated and fragile than conventional industrial platforms. The effective management of such a system relies heavily on the resilience of the network, especially the communication part. Imperative as resilient communication is, there is not enough attention from literature and a standardized framework is still missing. In awareness of these, this paper intends to provide a systematic overview of resilience in IIoT with a communication perspective, aiming to answer the questions of why we need it, what it is, how to enhance it, and where it can be applied. Specifically, we emphasize the urgency of resilience studies via examining existing literature and analyzing malfunction data from a real satellite communication system. Resilience-related concepts and metrics, together with standardization efforts are then summarized and discussed, presenting a basic framework for analyzing the resilience of the system before, during, and after disruptive events. On the basis of the framework, key resilience concerns associated with the design, deployment, and operation of IIoT are briefly described to shed light on the methods for resilience enhancement. Promising resilient applications in different IIoT sectors are also introduced to highlight the opportunities and challenges in practical implementations.