Autonomous driving systems (ADS) are revolutionizing transportation by reducing human intervention, improving operational efficiency, and enhancing safety. Large-scale language models (LLMs) have been integrated to support high-level decision-making in ADSs through powerful reasoning, direction-following, and communication capabilities. However, LLM-based single-agent ADSs face three major challenges: limited cognition, insufficient collaboration, and high computational demands. To address these challenges, recent LLM-based multi-agent ADSs leverage language-based communication and coordination to enhance inter-agent collaboration. This paper presents a state-of-the-art survey of this emerging intersection between NLP and multi-agent ADSs. We begin with a background introduction to related concepts and categorize existing LLM-based methods based on various agent interaction modes. We then discuss agent-human interaction in scenarios where LLM-based agents interact with humans. Finally, we summarize key application areas, datasets, and challenges to support future research.