This study investigates the characteristics of geopolitical risks, the connectedness among geopolitical risks, and the synchronization between geopolitical risks and global economic variables by employing Dynamic Factor Models, Spillover Indices, Connectedness Analysis, and the DCC-GARCH model. The empirical findings suggest that the geopolitical risk components— common, regional, and country-specific factors—estimated through the DFM are likely to act as short-term shock factors. Additionally, the connectedness analysis using the DFM-based variance decomposition and spillover indices reveals that geopolitical risks in the Americas, Europe, and Asia-Oceania are significantly influenced by external shocks, whereas the Middle East and Africa tend to act as net transmitters of geopolitical risks. Furthermore, within the Asia-Oceania region, geopolitical risks originating from other countries in the same region have a relatively greater influence, indicating strong intra-regional spillover effects. The time-varying correlations estimated via the DCC-GARCH model confirm that the comovement or decoupling between geopolitical risks and economic variables evolves dynamically over time. While increases in geopolitical risk generally deteriorate the global economic environment, in some instances, rising geopolitical risks in foreign countries serve as a factor that improves economic conditions in other nations.