Large Language Models (LLMs) are transforming healthcare through LLM-based agents that can understand and assist with medical tasks. This survey examines the architectures, applications, and challenges of LLM-based agents in medicine. We analyze key components including system profiles, clinical planning, medical reasoning frameworks, and external capacity enhancement. The survey covers major applications in clinical decision support, medical documentation, training simulations, and healthcare service optimization, along with evaluation frameworks and metrics. While these agents show promise in enhancing healthcare delivery, challenges remain in hallucination management, multimodal integration, implementation, and ethics. We conclude by highlighting future directions in medical reasoning, physical system integration, and training simulations, providing researchers and practitioners with a structured overview of the field’s current state and prospects.