AI and Big Data are transforming the healthcare industry by providing a newer, more individualized, prognostic, and less costly approach to health care. This survey focuses on the applications of machine learning (ML), deep learning (DL), and natural language processing (NLP) in combining with healthcare data resources, including electronic health records, medical image, and wearable devices. Integration of both AI and Big Data improves diagnosis, disease prevention, support for treatment of individuals and groups, as well as population health. Some of these are Early and accurate diagnosis of diseases, use of AI in drugs targeting, detection of cancer, heart diseases, and other chronic diseases AI in resource utilization for effective population health management, and personalized medicine solutions. Nonetheless, there are some key issues we will have to solve in the future, like data protection and security, bias issues, and data quality and availability issues. Other related issues, such as ethical aspects of AI decision-making processes, including impartiality and openness, are important for enhancing trust in these systems. This paper also describes future trends in AI and Big data including Explainable AI and Federated learning and new emerging area AIdriven drug discovery and application of AI on future pandemic preparedness. In summary, AI together with Big Data is functioning to revolutionize the healthcare domain, which has immense prospects to enhance its efficiency and benefits for patients in the future years.