<p>The growing demand for Artificial Intelligence (AI) in healthcare systems requires a comprehensive understanding of trust and reliability to guarantee patient protection, confidentiality, and welfare. While AI has a lot of potential for the healthcare industry, there are issues to overcome in its actual use, such as issues with reliability and trust. In order to mitigate these issues, a crucial field of study called AI Trust Frameworks has evolved, with the goal of defining criteria and recommendations for assessing and guaranteeing the accuracy of AI systems used in healthcare. This article provides an in-depth analysis of the current state, methods, and essential components of the current AI trust frameworks in healthcare applications by answering three research questions. These include highlighting the importance of Trust in AI-powered healthcare Applications, various factors that contribute to the evaluation of trustworthiness in AI healthcare systems, and challenges commonly employed in this research domain. The study also looks at potential future avenues for the creation and improvement of AI Trust Frameworks, highlighting the necessity of ongoing validation, stakeholder involvement, and interdisciplinary collaboration to meet challenging needs in healthcare. The findings from this survey seek to assist scholars who are eager to investigate AI Trust Frameworks in Healthcare. Thus, researchers, decision-makers, and medical professionals who are trying to understand the complex landscape of AI may find this survey to be a valuable resource.</p>