New evidence is presented on the sudden shift in the sentiment of market participants with the outbreak of the sovereign debt crisis. Since volatility reflects the extent to which the market evaluates the arrival of new information and provides useful insights into the dynamics of EMU sovereign debt markets, we analyze their spillovers. To that end, we first examine the unconditional patterns during the full sample (April 1999-January 2014) using a measure recently proposed by Diebold and Yilmaz (2012). Second, we make use of a dynamic analysis to evaluate net directional volatility spillovers for each of the eleven countries under stud and to determine whether core and peripheral markets present differences both before and during the crisis periods. Finally, we apply a panel analysis to empirically investigate the determinants of net directional spillovers of this kind. Our results suggest that slightly more than half of the total variance of the forecast errors is explained by shocks across countries rather than by idiosyncratic shocks. Besides, they give further support to the idea that during the pre-crisis period, most of the triggers in the volatility spillovers were central countries - peripheral countries imported credibility from them - while during the crisis, peripheral countries became the dominant transmitters.