The utilization of large language models (LLMs) for Healthcare has generated both excitement and concern due to their ability to effectively respond to free-text queries with certain professional knowledge. This survey outlines the capabilities of the currently developed Healthcare LLMs and explicates their development process, to provide an overview of the development road map from traditional Pretrained Language Models (PLMs) to LLMs. Specifically, we first explore the potential of LLMs to enhance the efficiency and effectiveness of various Healthcare applications highlighting both the strengths and limitations. Secondly, we conduct a comparison between the previous PLMs and the latest LLMs, and summarize related Healthcare training data, learning methods, and usage. Finally, the unique concerns associated with deploying LLMs are investigated, particularly regarding fairness, accountability, transparency, and ethics. Besides, we support researchers by compiling a collection of open-source resources1. Summarily, we contend that a significant paradigm shift is underway, transitioning from PLMs to LLMs. This shift encompasses a move from discriminative AI approaches to generative AI approaches, as well as a move from model-centered methodologies to datacentered methodologies. We determine that the biggest obstacle of using LLMs in Healthcare are fairness, accountability, transparency and ethics.