Large Language Models (LLMs) have significantly advanced communications fields, such as Telecom Q&A, mathematical modeling, and optimization solving. However, LLMs encounter an inherent issue known as hallucination, i.e., generating fact-conflicting or irrelevant content. This problem critically undermines the applicability of LLMs in communication systems yet has not been systematically explored. Hence, this article provides a comprehensive review of LLM applications in communications, with a p