With the power of parallel processing, large datasets,and fast computational resources, deep neural networks (DNNs) have outperformed highly trained and experienced human experts in medical applications. However, the large global community of healthcare professionals, many of whom routinely face potentially life-or-death outcomes with complex medicolegal consequences, have yet to embrace this powerful technology. The major problem is that most current AI solutions function as a metaphorical black-box positioned between input data and output decisions without a rigorous explanation for their internal processes. With the goal of enhancing trust and improving acceptance of AI-based technology in clinical medicine, there is a large and growing effort to address this challenge using eXplainable AI (XAI), a set of techniques, strategies, and algorithms with an explicit focus on explaining the “hows and whys” of DNNs. Here, we provide a comprehensive review of the state-of-the-art XAI techniques concerning healthcare applications and discuss current challenges and future directions. We emphasize the strengths and limitations of each category, including image, tabular, and textual explanations, and explore a range of evaluation metrics for assessing the effectiveness of XAI solutions. Finally, we highlight promising opportunities for XAI research to enhance the acceptance of DNNs by the healthcare community.