Large Language Models (LLMs) have demonstrated remarkable capabilities across various domains, including their emerging role in mitigating threats to human life, infrastructure, and the environment during natural disasters. Despite increasing research on disaster-focused LLMs, there remains a lack of systematic reviews and in-depth analyses of their applications in natural disaster management. To address this gap, this paper presents a comprehensive survey of LLMs in disaster response, introducing a taxonomy that categorizes existing works based on disaster phases and application scenarios. By compiling public datasets and identifying key challenges and opportunities, this study aims to provide valuable insights for the research community and practitioners in developing advanced LLM-driven solutions to enhance resilience against natural disasters.