The European Union set three goals (for energy efficiency, share of renewable energy sources, and greenhouse gas emissions) in the Energy 2020 document emphasising the importance of joint actions. This study investigates the 28 members' progression in the light of these commitments, between 2001 and 2012. Applying the methodology of sigma and beta convergence, we prove the convergence progress across the member states, but the result of gamma convergence modifies it: we conclude that differences remained in the European Union between 2001 and 2012 but the extent of the differences decreased significantly. The renewables ratio shows the fastest convergence rate. With energy intensity and emissions these positive processes are affected negatively by the financial crisis, causing temporary divergence. Calculating convergence clubs raises awareness of differences between the old and new member states.