The integration of large language models (LLMs), such as ChatGPT, into computer science education has opened new avenues for enhancing teaching and learning. Although the existing literature has explored their use in various domains, the adoption of LLMs in the education of database management systems (DBMS) remains limited. This study presents a systematic literature review (SLR) examining how LLMs are currently used in DBMS courses for tasks such as SQL query assistance, ER diagram feedback, relational algebra generation, and automated grading. We analyze the educational applications, accuracy, and perceptions surrounding these tools. Our findings show that while LLMs offer significant support in teaching and learning, challenges persist around feedback quality, grading consistency, and over-reliance on LLMs output. The review concludes with recommendations for future research, including the need for empirical evaluations, improved AI-human collaboration frameworks, and fine-tuning of LLMs for DBMS-specific tasks.