Since the release of ChatGPT and GPT-4, large language models (LLMs) and multimodal large language models (MLLMs) have attracted widespread attention for their exceptional capabilities in understanding, reasoning, and generation, introducing transformative paradigms for integrating artificial intelligence into medicine. This survey provides a comprehensive overview of the development, principles, application scenarios, challenges, and future directions of LLMs and MLLMs in medicine. Specifically, it begins by examining the paradigm shift, tracing the transition from traditional models to LLMs and MLLMs, and highlighting the unique advantages of these LLMs and MLLMs in medical applications. Next, the survey reviews existing medical LLMs and MLLMs, providing detailed guidance on their construction and evaluation in a clear and systematic manner. Subsequently, to underscore the substantial value of LLMs and MLLMs in healthcare, the survey explores five promising applications in the field. Finally, the survey addresses the challenges confronting medical LLMs and MLLMs and proposes practical strategies and future directions for their integration into medicine. In summary, this survey offers a comprehensive analysis of the technical methodologies and practical clinical applications of medical LLMs and MLLMs, with the goal of bridging the gap between these advanced technologies and clinical practice, thereby fostering the evolution of the next generation of intelligent healthcare systems.