ChatGPT has drawn considerable attention from both the general public and domain experts with its remarkable text generation capabilities. This has subsequently led to the emergence of diverse applications in the field of biomedicine and health. In this work, we examine the diverse applications of large language models (LLMs), such as ChatGPT, in biomedicine and health. Specifically we explore the areas of biomedical information retrieval, question answering, medical text summarization, information extraction, and medical education, and investigate whether LLMs possess the transformative power to revolutionize these tasks or whether the distinct complexities of biomedical domain presents unique challenges. Following an extensive literature survey, we find that significant advances have been made in the field of text generation tasks, surpassing the previous state-of-the-art methods. For other applications, the advances have been modest. Overall, LLMs have not yet revolutionized biomedicine, but recent rapid progress indicates that such methods hold great potential to provide valuable means for accelerating discovery and improving health. We also find that the use of LLMs, like ChatGPT, in the fields of biomedicine and health entails various risks and challenges, including fabricated information in its generated responses, as well as legal and privacy concerns associated with sensitive patient data. We believe this survey can provide a comprehensive and timely overview to biomedical researchers and healthcare practitioners on the opportunities and challenges associated with using ChatGPT and other LLMs for transforming biomedicine and health.