The increasing frequency and severity of extreme weather events, driven by global climate change, makes ensuring the resilience of power systems a pressing challenge. To comprehensively analyze the operation of power systems under extreme weather conditions, this study employs bibliometric and BERTopic modeling methods. Based on 2,076 research articles retrieved from the Web of Science database between 2001 and 2025, we analyzed publication trends, identified leading countries and institutions, and revealed core research topics. Our results indicate that the number of publications has shown an accelerated growth phase since 2016. The USA and China are the dominant research forces, with the highest number of publications and citations, and the highest publication impact. Furthermore, topic modeling identified 11 core research clusters, among which “resilience framework and restoration strategies”, “climate risks in the context of energy transition”, and “hydropower and climate risks” form the foundational pillars of current research. Finally, this study proposes an integrated framework, points out future research directions, including multi-technology synergy, data-driven methods, and more. This research systematically maps the directions within the field and provides a reference for guiding future in-depth studies aimed at enhancing the resilience of power systems to extreme weather.