Database management systems (DBMSs) are the cornerstone of modern information infrastructure, and their reliability directly impacts data security and business continuity. As system complexity increases, bugs in DBMSs can lead to data corruption, information leakage, or even system failures. In recent years, fuzzing has become an efficient automated technique for detecting bugs and has been widely used in DBMS reliability testing, yielding significant results. However, traditional fuzzing approaches typically rely on simple rules or pattern-based test case generation, which makes it difficult to construct complex scenarios with deeper semantic understanding. Consequently, they remain insufficient for covering complex interaction paths and triggering deep-seated bugs in DBMSs. Meanwhile, the rapid advancement of large language models (LLMs) has brought new opportunities for DBMS testing. With strong semantic understanding, contextual reasoning, and self-learning capabilities, LLMs can generate diverse and semantically valid SQL test cases, assist with result validation and defect analysis, and significantly improve the automation and intelligence of DBMS reliability testing, enabling the discovery of deep-seated defects in databases. This paper presents a systematic review of research progress on the application of LLMs in DBMS reliability testing. The latest advances in LLM-based testing frameworks are analyzed in terms of test case generation, result validation, coverage feedback, and testing optimization. The effectiveness and limitations of existing studies are evaluated, and future development directions for DBMS reliability testing are discussed.