Climate change increases the risks of natural hazards. The latest report of the United Nations Environment Programme (UNEP) released last October 2022 alleges the increasing climate change is contributed to by anthropogenic, that is, human-made activities. Its projected global temperature increase will severely affect everyone's living conditions and economy. As the most critical operation for managing and transferring climate risks and supporting climate action, the insurance industry is confronting the significant challenges arising from the foreseeable climate change in the next decades. Appropriate adaptation practices from the insurance industry are, thus, vital for its resilience and sustainability. However, there is a lack of an understanding of the climate actions the insurance industry is taking. More importantly, no systematic assessments of insurers' latest adaptation practices to better respond to the risks and opportunities arising from climate change exist. Therefore, this research aims to fill this gap by conducting a structured literature review and proposing a typology for differentiating the types of insurers' engagement in responding to climate change. Aiming to precisely identify the most influential literature, bibliometrics, a quantitative analysis of 927 articles on climate change and the insurance industry was conducted to determine the main topics, authors and associations, major publication countries and highly cited papers. Twenty-five articles were subsequently selected for the structured literature review. Three adaptation types: a climate change advocate, a risk management expert, and an innovative solution provider, were developed as the findings. The benefits and challenges encountered by each type of adaptation practice were discussed in depth to imply the future enhancement of the industry's role as a sustainable partner in battling the challenges of climate risks.