Traditional industry performs their operations with conventional technologies such as mechanical machines, standalone computers, and human resources. The Industrial Revolution changed industrial operations with the deployment of emerging technologies and fewer human resources for industrial operations and management. In the smart industry, the industrial Internet of Things (IIoT) is used for data collection, processing, and analysis. IIoT is also used for automation, remote monitoring, and communication of devices with each other. The smart industry uses various devices, servers, applications, protocols, and continuous connectivity with the internet; its attack surface has increased due to multiple threats and vulnerabilities. IIoT is exposed to various cyber-attacks such as ransomware, cross-site scripting, Man in the middle, sniffing, and spoofing. Intrusion detection systems (IDS) have been used as technical control for the cyber defense of digital assets and services. IDS has been used with misuse and anomaly-based methods. Misuse methods are not practicable for threat mitigation in smart industry due to their limitation, such as the detection of known attacks which are stored in signature database; however, emerging attacks, such as ransomware or DDoS use various strategies to initiate cyber-attacks on systems. Deep learning (DL) based IDS are more efficient due to its high-performance metrics. In this paper, we have discussed IIoT importance in the smart industry and cybersecurity challenges related to IIoT. Furthermore, we have briefly described IDS classification and IIoT datasets for the development of DL-based systems. Finally, we have provided literature on DL-based security solutions for threat mitigation in IIoT environments.