<p>Large Language Models (LLM) have gained significant traction in recent years, attracting widespread interest from both academia and industry due to their remarkable ability to process and generate human language. Their potential in healthcare is especially compelling and promising to revolutionize compute-intensive tasks such as patient care, clinical decision making, and medical research. However, the full extent of the impact of LLM on healthcare remains largely unexplored. This paper systematically analyzes the role of these models in healthcare, focusing on their potential to transform key areas such as diagnostics, personalized medicine, and operational efficiency. Through a comprehensive review of the existing literature, we have developed taxonomies to categorize the applications and requirements of these models in healthcare, highlighting their unique capabilities in information processing. The survey delves into the background and enabling technologies that support these models, examining the architectural considerations necessary for their successful integration into healthcare systems. In addition, it addresses critical security and privacy concerns, proposing defense mechanisms to ensure the safe and ethical deployment of LLMs in medical environments. This paper provides a panoramic view of the LLM paradigm in healthcare by highlighting open issues and future research directions. Our aim is to guide researchers and practitioners in understanding the current research landscape, identifying opportunities and challenges, and making informed decisions when designing LLM applications for healthcare. We advocate for enhancing accuracy, reliability, and interpretability while reducing computational costs and expanding LLM accessibility to improve healthcare delivery and advance medical research.</p>