Query understanding in Conversational Information Seeking (CIS) involves accurately interpreting user intent through context-aware interactions. This includes resolving ambiguities, refining queries, and adapting to evolving information needs. Large Language Models (LLMs) enhance this process by interpreting nuanced language and adapting dynamically, improving the relevance and precision of search results in real-time. In this tutorial, we explore advanced techniques to enhance query understanding in LLM-based CIS systems. We delve into LLM-driven methods for developing robust evaluation metrics to assess query understanding quality in multi-turn interactions, strategies for building more interactive systems, and applications like proactive query management and query reformulation. We also discuss key challenges in integrating LLMs for query understanding in conversational search systems and outline future research directions. Our goal is to deepen the audience's understanding of LLM-based conversational query understanding and inspire discussions to drive ongoing advancements in this field.