This paper assesses the convergence of the EU-28 countries towards their common goal of 20% in the renewable energy share indicator by year 2020. The potential presence of clubs of convergence towards different steady state equilibria is also analyzed from both the standpoints of global convergence to the 20% goal and specific convergence to the various targets assigned to Member States. Two clubs of convergence are detected in the former case, each corresponding to different RES targets. A probit model is also fitted with the aim of better understanding the determinants of club membership, that seemingly include real GDP per capita, expenditure on environmental protection, energy dependence, and nuclear capacity, with all of them having statistically significant effects. Finally, convergence is also analyzed separately for the transport, heating and cooling, and electricity sectors.