This survey provides a comprehensive review of research on multi-turn dialogue systems, focusing on those based on large language models (LLMs). The paper aims to: 1. Summarize existing LLMs and methods for adapting them to downstream tasks. 2. Elaborate on recent advances in multi-turn dialogue systems, covering both open-domain dialogue (ODD) and task-oriented dialogue (TOD) systems, along with datasets and evaluation metrics. 3. Discuss future emphasis and recent research problems arising from the development of LLMs and the increasing demands on multi-turn dialogue systems. The survey is organized into several sections, including an introduction to multi-turn dialogue systems, a detailed exposition of prevalent LLMs, methods for adapting LLMs to downstream tasks, and discussions on TOD and ODD systems. It also covers fine-tuning techniques, prompt engineering, and the challenges and future directions in LLM-based multi-turn dialogue systems. The paper highlights the importance of LLMs in enhancing the performance of multi-turn dialogue systems and provides insights into the latest advancements and research trends in this field.This survey provides a comprehensive review of research on multi-turn dialogue systems, focusing on those based on large language models (LLMs). The paper aims to: 1. Summarize existing LLMs and methods for adapting them to downstream tasks. 2. Elaborate on recent advances in multi-turn dialogue systems, covering both open-domain dialogue (ODD) and task-oriented dialogue (TOD) systems, along with datasets and evaluation metrics. 3. Discuss future emphasis and recent research problems arising from the development of LLMs and the increasing demands on multi-turn dialogue systems. The survey is organized into several sections, including an introduction to multi-turn dialogue systems, a detailed exposition of prevalent LLMs, methods for adapting LLMs to downstream tasks, and discussions on TOD and ODD systems. It also covers fine-tuning techniques, prompt engineering, and the challenges and future directions in LLM-based multi-turn dialogue systems. The paper highlights the importance of LLMs in enhancing the performance of multi-turn dialogue systems and provides insights into the latest advancements and research trends in this field.