Artificial intelligence (AI) technology has advanced rapidly in recent years, with large language models (LLMs) emerging as a significant breakthrough. LLMs are increasingly making an impact across various industries, with the medical field standing out as the most prominent application area. This paper systematically reviews the up-to-date research progress of LLMs in the medical field, providing an in-depth analysis of training techniques for large medical models, their adaptation in healthcare settings, related applications, as well as their strengths and limitations. Furthermore, it innovatively categorizes medical LLMs into three distinct types based on their training methodologies and classifies their evaluation approaches into two categories. Finally, the study proposes solutions to existing challenges and outlines future research directions based on identified issues in the field of medical LLMs. By systematically reviewing previous and advanced research findings, we aim to highlight the necessity of developing medical LLMs, provide a deeper understanding of their current state of development, and offer clear guidance for subsequent research.