User simulation has long played a vital role in computer science due to its potential to support a wide range of applications. Language, as the primary medium of human communication, forms the foundation of social interaction and behavior. Consequently, simulating conversational behavior has become a key area of study. Recent advancements in large language models (LLMs) have significantly catalyzed progress in this domain by enabling high-fidelity generation of synthetic user conversation. In this paper, we survey recent advancements in LLM-based conversational user simulation. We introduce a novel taxonomy covering user granularity and simulation objectives. Additionally, we systematically analyze core techniques and evaluation methodologies. We aim to keep the research community informed of the latest advancements in conversational user simulation and to further facilitate future research by identifying open challenges and organizing existing work under a unified framework.