This study examines the risk spillovers between energy futures prices and Europe-based carbon futures contracts. We use a Markov regime-switching dynamic correlation, generalized autoregressive conditional heteroscedasticity (MS-DCC-GARCH) model in order to capture the time variations and structural breaks in the spillovers. We further evaluate the optimal weights, hedging effectiveness, and dynamic hedging strategies for the MS-DCC-GARCH model based on both the regime-dependent and regime-independent optimal hedge ratios. We finally complement our analysis by examining the in- and out-of sample hedging performances for alternative strategies. Our results mainly show significant volatility and time-varying risk transmission from energy markets to carbon market. We also find that spot and futures segments of the emission markets exhibit time-varying correlations and volatile hedging effectiveness. The subsample estimates show significant changes in the hedge effectiveness over the different phases of the European carbon market. These results have important investment and policy implications. •Risk spillovers between energy and carbon futures prices are studied.•We make use of a Markov regime-switching DCC-GARCH.•Optimal weights, hedging effectiveness, and dynamic hedging strategies are evaluated.•There exists significant time-varying risk transmission from energy to carbon markets.•Carbon spot and futures segments exhibit volatile hedging effectiveness.