Currently, most applications in the Industrial Internet of Things (IIoT) still rely on CNN-based neural networks. Although Transformer-based large models (LMs), including language, vision, and multimodal models, have demonstrated impressive capabilities in AI-generated content (AIGC), their application in industrial domains, such as detection, planning, and control, remains relatively limited. Deploying pre-trained LMs in industrial environments often encounters the challenge of stability and plasticity due to the complexity of tasks, the diversity of data, and the dynamic nature of user demands. To address these challenges, the pre-training and fine-tuning strategy, coupled with continual learning, has proven to be an effective solution, enabling models to adapt to dynamic demands while continuously optimizing their inference and decision-making capabilities. This paper surveys the integration of LMs into IIoT-enhanced General Industrial Intelligence (GII), focusing on two key areas: LMs for GII and LMs on GII. The former focuses on leveraging LMs to provide optimized solutions for industrial application challenges, while the latter investigates continuous optimization of LMs learning and inference capabilities in collaborative scenarios involving industrial devices, edge computing, and cloud computing. This paper provides insights into the future development of GII, aiming to establish a comprehensive theoretical framework and research direction for GII, thereby advancing GII towards a more general and adaptive future.