Driven by the rapid advancements of Large Language Models (LLMs), LLM-based agents have emerged as powerful intelligent systems capable of human-like cognition, reasoning, and interaction. These agents are increasingly being deployed across diverse real-world applications, including student education, scientific research, and financial analysis. However, despite their remarkable potential, LLM-based agents remain vulnerable to hallucination issues, which can result in erroneous task execution and undermine the reliability of the overall system design. Addressing this critical challenge requires a deep understanding and a systematic consolidation of recent advances on LLM-based agents. To this end, we present the first comprehensive survey of hallucinations in LLM-based agents. By carefully analyzing the complete workflow of agents, we propose a new taxonomy that identifies different types of agent hallucinations occurring at different stages. Furthermore, we conduct an in-depth examination of eighteen triggering causes underlying the emergence of agent hallucinations. Through a detailed review of a large number of existing studies, we summarize approaches for hallucination mitigation and detection, and highlight promising directions for future research. We hope this survey will inspire further efforts toward addressing hallucinations in LLM-based agents, ultimately contributing to the development of more robust and reliable agent systems.