Sustainability is now a priority issue that governments, businesses and society in general must address in the short term. In their role as major global institutional investors and risk managers, insurance companies and pension funds are strategic players in building socio-economic and sustainable development. To gain a comprehensive understanding of the current state of action and research on environmental, social and governance (ESG) factors in the insurance and pension sectors, we conduct a systematic literature review. We rely on the PRISMA protocol and analyze 1 731 academic publications available in the Web of Science database up to the year 2022 and refer to 23 studies outside of scientific research retrieved from the websites of key international and European organizations. To study the corpus of literature, we introduce a classification framework along the insurance value chain including external stakeholders. The main findings reveal that risk, underwriting and investment management are the most researched areas among the nine categories considered in our framework, while claims management and sales tend to be neglected. Regarding ESG factors, climate change, as part of the environmental factor, has received the most attention in the literature. After reviewing the literature, we summarize the main sustainability issues and potential related actions. Given the current nature of the sustainability challenges for the insurance sector, this literature review is relevant to academics and practitioners alike.