In this study, we investigated the effects of geopolitical risk (GPR) on commodity future returns by computing the conditional value at risk (CoVaR) and delta CoVaR using time-varying and static bivariate copula models. Our results indicate that there is generally a positive dependence between commodity returns and changes in GPR. Empirical evidence also suggests that there are only upside risk spillovers from GPR to commodity markets. The delta CoVaR results locate the greatest systemic risk in heating oil and maize commodities. Future research avenues, as well as policy and practical implications, are outlined.