In recent years, artificial intelligence (AI) technology has been used in most if not all domains and has greatly benefited our lives. While AI can accurately extract critical features and valuable information from large amounts of data to help people complete tasks faster, there are growing concerns about the non-transparency of AI in the decision-making process. The emergence of explainable AI (XAI) has allowed humans to better understand and control AI systems, which is motivated to provide transparent explanations for the decisions made by AI. This article aims to present a comprehensive overview of recent research on XAI approaches from three well-defined taxonomies. We offer an in-depth analysis and summary of the status and prospects of XAI applications in several key areas where reliable explanations are urgently needed to avoid mistakes in decision-making. We conclude by discussing XAI’s limitations and future research directions.