Conversational search enables multi-turn interactions between users and systems to fulfill users' complex information needs. During this interaction, the system should understand the users' search intent within the conversational context and then return the relevant information through a flexible, dialogue-based interface. The recent powerful large language models (LLMs) with capacities of instruction following, content generation, and reasoning, attract significant attention and advancements, providing new opportunities and challenges for building up intelligent conversational search systems. This tutorial aims to introduce the connection between fundamentals and the emerging topics revolutionized by LLMs in the context of conversational search. It is designed for students, researchers, and practitioners from both academia and industry. Participants will gain a comprehensive understanding of both the core principles and cutting-edge developments driven by LLMs in conversational search, equipping them with the knowledge needed to contribute to the development of next-generation conversational search systems.