This survey provides a comprehensive overview of Foundation Models (FMs) in the healthcare domain, focusing on their history, learning strategies, flagship models, applications, and challenges. FMs are large-scale deep-learning models trained on extensive datasets using self-supervised techniques, which have been successfully applied across various healthcare domains, including natural language processing (NLP), computer vision, graph learning, biology, and omics. The survey highlights the evolution of AI and deep learning models, particularly the introduction of transformers, and their impact on FMs. It discusses the key enablers of FMs, such as training data, base models, transfer learning, and scale, and explores how models like BERT and GPT families are reshaping healthcare domains. The survey also provides a detailed taxonomy of healthcare applications facilitated by FMs, including clinical NLP, medical image analysis, and omics data. Despite the promising opportunities, challenges such as cost, interpretability, validation, and scale are discussed in detail. The survey outlines potential future directions to advance the deployment and mitigate risks associated with FMs in healthcare.This survey provides a comprehensive overview of Foundation Models (FMs) in the healthcare domain, focusing on their history, learning strategies, flagship models, applications, and challenges. FMs are large-scale deep-learning models trained on extensive datasets using self-supervised techniques, which have been successfully applied across various healthcare domains, including natural language processing (NLP), computer vision, graph learning, biology, and omics. The survey highlights the evolution of AI and deep learning models, particularly the introduction of transformers, and their impact on FMs. It discusses the key enablers of FMs, such as training data, base models, transfer learning, and scale, and explores how models like BERT and GPT families are reshaping healthcare domains. The survey also provides a detailed taxonomy of healthcare applications facilitated by FMs, including clinical NLP, medical image analysis, and omics data. Despite the promising opportunities, challenges such as cost, interpretability, validation, and scale are discussed in detail. The survey outlines potential future directions to advance the deployment and mitigate risks associated with FMs in healthcare.