Large language models (LLMs) are increasingly being explored as complementary tools in smart manufacturing, offering advanced capabilities in semantic reasoning, knowledge integration, multimodal interpretation, and decision support. However, their role in industrial fault diagnosis (FD) remains fragmented and insufficiently characterised. This paper reviews recent studies at the intersection of LLMs and FD and proposes an application-centric taxonomy reflecting how LLMs are deployed in diagnostic workflows. Seven functional roles are identified: knowledge-based diagnosis, data-centric fault interpretation, automated signal processing, predictive-maintenance decision support, industrial knowledge fusion via RAG and knowledge graphs, multimodal fault analysis, and autonomous diagnostic agents. The findings indicate that LLMs do not replace conventional signal-processing or deep-learning models but provide a complementary cognitive layer enabling contextualised reasoning. Key challenges such as hallucination, reliability, confidentiality, real-time constraints, and limited physical grounding are analysed alongside opportunities in multimodal industrial foundation models, physics-aligned LLMs, edge copilots, and autonomous maintenance agents.