In this study, we comprehensively examine the volatility term structures in commodity markets. We model state-dependent spillovers in principal components (PCs) of the volatility term structures of different commodities, as well as that of the equity market. We detect strong economic links and a substantial interconnectedness of the volatility term structures of commodities. Accounting for intra-commodity-market spillovers significantly improves out-of-sample forecasts of the components of the volatility term structure. Spillovers following macroeconomic news announcements account for a large proportion of this forecast power. There thus seems to be substantial information transmission between different commodity markets.