The rapid advancement of Large Language Models (LLMs) has opened new possibilities in Multi-Robot Systems (MRS), enabling enhanced communication, task allocation and planning, and human-robot interaction. Unlike traditional single-robot and multi-agent systems, MRS poses unique challenges, including coordination, scalability, and real-world adaptability. This survey provides the first dedicated review of LLM integration into MRS. It systematically categorizes their applications across high-level task allocation, mid-level motion planning, low-level action generation, and human intervention. We highlight key applications in diverse domains, such as household robotics, construction, formation control, target tracking, and robot games, showcasing the versatility and transformative potential of LLMs in MRS. Furthermore, we examine the challenges that limit adapting LLMs to MRS, including mathematical reasoning limitations, hallucination, latency issues, and the need for robust benchmarking systems. Finally, we outline opportunities for future research, emphasizing advancements in fine-tuning, reasoning techniques, and task-specific models. This survey aims to guide researchers in the intelligence and real-world deployment of MRS powered by LLMs. Given the rapidly evolving nature of research in the field, we continuously update the paper list in the open-source GitHub repository.