The adoption of artificial intelligence (AI) in healthcare has the potential to transform patient outcomes and optimize clinical workflows. However, trust in AI systems is a critical factor in ensuring their successful integration into healthcare systems. This paper reviews the literature on the impact of trust in adopting AI in healthcare, exploring how trust influences user acceptance, adoption, and utilization of AI technologies. Additionally, the paper discusses the factors that contribute to trust in AI systems, including system transparency, explainability, and reliability, as well as the potential ethical concerns associated with AI adoption. The findings of this paper suggest that building trust in AI systems is essential for their successful integration into healthcare, and that policymakers and healthcare organizations need to prioritize efforts to foster trust in AI among healthcare professionals and patients alike.