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Recent years have seen a dramatic increase in the number of and severity of natural disasters, driven in part by climate change and urbanization. Artificial Intelligence (AI) appears to be a promising new technology that can transform disaster risk management (DRM) and provide new opportunities for prediction, monitoring, response, and recovery. The present study performs a bibliometric review of applications of AI to DRM, from a total collection of 7842 scientific articles extracted from Scopus, Web of Science and OpenAlex databases from the year 2003 to the year 2025. Exploring the trends of publications, authorship, international collaboration, and research topics, the study reveals the development and current status of AI incorporating disaster management. The results illustrate an apparent growth in interest in the field of science, how machine learning and deep learning methodologies are leading, and the raise of geospatial AI, remote sensing, and social media analysis in disaster preparedness and response. Other issues including data quality, ethics, technology and trust in AI systems are also considered. This study offers helpful perspectives on the status quo and future development of AI-based DRMs.