This survey provides a comprehensive review of research on multi-turn dialogue systems, with a focus on those based on large language models (LLMs). The paper aims to summarize existing LLMs and methods for adapting them to downstream tasks, elaborate on recent advances in multi-turn dialogue systems, including both open-domain (ODD) and task-oriented (TOD) systems, and discuss future research directions. It covers LLMs, their architectures, fine-tuning techniques, prompt engineering, and their applications in dialogue systems. LLMs are characterized by their massive scale and ability to generate accurate language representations. They include decoder-only models like GPT series, encoder-only models like BERT and RoBERTa, and encoder-decoder models like BART and T5. These models have been adapted for various tasks through full fine-tuning, parameter-efficient fine-tuning (PEFT), and prompt engineering. Full fine-tuning optimizes all model parameters to adapt to specific tasks, while PEFT methods, such as adapters and LoRA, adjust only a portion of the parameters, making them more efficient. Prompt engineering techniques, including prompt tuning and tuning-free prompting, enhance model performance by modifying input prompts rather than the model itself. In task-oriented dialogue systems, pipeline-based approaches involve modules for natural language understanding (NLU), dialogue state tracking (DST), policy learning (PL), and natural language generation (NLG). These systems are designed to handle specific domain tasks, such as hotel booking or restaurant recommendations. Recent advancements include joint intent detection and slot filling, as well as the use of large language models for more efficient and accurate dialogue management. The survey also discusses challenges and future directions in the development of LLM-based dialogue systems.This survey provides a comprehensive review of research on multi-turn dialogue systems, with a focus on those based on large language models (LLMs). The paper aims to summarize existing LLMs and methods for adapting them to downstream tasks, elaborate on recent advances in multi-turn dialogue systems, including both open-domain (ODD) and task-oriented (TOD) systems, and discuss future research directions. It covers LLMs, their architectures, fine-tuning techniques, prompt engineering, and their applications in dialogue systems. LLMs are characterized by their massive scale and ability to generate accurate language representations. They include decoder-only models like GPT series, encoder-only models like BERT and RoBERTa, and encoder-decoder models like BART and T5. These models have been adapted for various tasks through full fine-tuning, parameter-efficient fine-tuning (PEFT), and prompt engineering. Full fine-tuning optimizes all model parameters to adapt to specific tasks, while PEFT methods, such as adapters and LoRA, adjust only a portion of the parameters, making them more efficient. Prompt engineering techniques, including prompt tuning and tuning-free prompting, enhance model performance by modifying input prompts rather than the model itself. In task-oriented dialogue systems, pipeline-based approaches involve modules for natural language understanding (NLU), dialogue state tracking (DST), policy learning (PL), and natural language generation (NLG). These systems are designed to handle specific domain tasks, such as hotel booking or restaurant recommendations. Recent advancements include joint intent detection and slot filling, as well as the use of large language models for more efficient and accurate dialogue management. The survey also discusses challenges and future directions in the development of LLM-based dialogue systems.