Climate change refers to persistent alterations to global Earth's climate, such as a rise in global temperatures, which have reached unprecedented peaks in recent years. At the same time, global mean ocean‐and‐sea levels are on an upward trajectory. These climatic shifts significantly influence the frequency, intensity, and duration of extreme weather events, such as heatwaves, heavy precipitations, droughts, floods, and tropical cyclones, which represent substantial risks and challenges for the insurance industry. This paper delves into the profound impact of climate change on the insurance sector, with a particular focus on the agriculture, property, health, and life insurance industries. Our scientific approach consists in measuring climate change through an index composed of a basket of climate and weather‐related extremes, such as the Actuarial Climate Index™ (ACI) defined in and for North America, and its European counterparts, the Iberian ACI (IACI) and French ACI (FACI) climate indices. We discuss how these indices help quantify the impact of climate change on the balance sheets of insurance companies and, therefore, its impact on the sustainability of the insurance business. The paper underscores the pressing need for the insurance industry to adapt and strategically plan for the increasing risks associated with climate change.