This paper provides a detailed examination of the advancements and applications of large language models in the healthcare sector, with a particular emphasis on clinical applications. The study traces the evolution of LLMs from their foundational technologies to the latest developments in domain-specific models and multimodal integration. It explores the technical progression from encoder-based models requiring fine-tuning to sophisticated approaches that integrate textual, visual, and auditory data, thereby facilitating comprehensive AI solutions in healthcare. The paper discusses both the opportunities these technologies present for enhancing clinical efficiency and the challenges they pose in terms of ethics, data privacy, and implementation. Additionally, it critically evaluates the deployment strategies of LLMs, emphasizing the necessity of open-source models to ensure data privacy and adaptability within healthcare environments. Future research directions are proposed, focusing on empirical studies to evaluate the real-world efficacy of LLMs in healthcare and the development of open datasets for further research. This review aims to provide a comprehensive resource for both newcomers and multidisciplinary researchers interested in the intersection of AI and healthcare.