This study examines the dynamic relationship between changes in oil prices and the economic policy uncertainty index for a sample of both net oil-exporting and net oil-importing countries over the period 1997:01-2013:06. To achieve that, an extension of the Diebold and Yilmaz (2009, 2012) dynamic spillover index based on structural decomposition is employed. The results reveal that economic policy uncertainty (oil price shocks) responds negatively to aggregate demand oil price shocks (economic policy uncertainty shocks). Furthermore, during the Great Recession of 2007-2009, total spillovers increase considerably, reaching unprecedented heights. Moreover, in net terms, economic policy uncertainty becomes the dominant transmitter of shocks between 1997 and 2009, while in the post-2009 period there is a significant role for supply-side and oil specific demand shocks, as net transmitters of spillover effects. These results are important for policy makers, as well as, investors interested in the oil market. (authors' abstract)