Compound climatic or weather extremes, involving the simultaneous occurrence in different regions or consecutive climatic hazards in the same area, pose significant challenges to human society. While recent studies have made progress in understanding the physical processes behind these compound extremes, there remains a gap in comprehensively investigating their impacts. This becomes crucial in the context of global warming, requiring adaptive strategies to address changes in the characteristics of these events. Our research addresses this gap by utilizing impact databases to examine four types of compound extremes and evaluate their impacts (e.g., economic losses, number of dead or affected people). Initially, we will explore spatially compound cold spells in North America and wet-windy weather conditions in Europe. The second aspect of our project focuses on temporally compound extremes in Europe, specifically examining the succession of drought conditions and flood hazards. The third dimension of our work involves studying multivariate compound extremes, with a focus on concurrent drought and heatwaves in Europe. Lastly, we will investigate pre-conditioned compound extremes, such as the soil moisture deficit favoring the risk of extreme wildfires. Through this comprehensive approach, we aim to contribute valuable insights into the diverse impacts of compound climatic extremes. Our progress in predicting climatic hazards will support the development of effective adaptation strategies to mitigate their adverse effects on human societies and the environment.