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The demand for healthcare around the world is being amplified as a result of rising patient demand, an aging population, workforce shortages, and personalized healthcare. Traditional forms of AI have been successfully used in disciplines like medical imaging, diagnosis, and decision support but only complete discrete tasks, whereas there is no ability to understand the whole context in which they are being used or to integrate with regular healthcare operational tasks. Agentic AI enables smart systems to operate autonomously, establish objectives, and apply skills such as comprehension, reasoning, planning, memory, and task completion in complex healthcare environments. This paper provides an overview of the various applications of agentic AI in healthcare by reviewing the architectural frameworks, empirical validations, and specific clinical applications. Healthcare agents will be grouped by how smart they are and how they are used; recent research will be summarized, and important areas for more study—like testing in real healthcare settings, setting standards, getting regulatory approvals, and ensuring safety for agentic AI—will be pointed out. The results of this study show that agentic AI has a strong potential to help with clinical decision support, health care analytics, biomedical research, and providing quality long-term care. However, agentic AI has not yet achieved widespread use in routine practices because of insufficient evaluation of its effectiveness through the use of standardized methods. Lastly, this study offers avenues for future research to develop agentic AI systems for future healthcare delivery that are safe, scalable, interoperable, and ethically congruent.