In the wake of the economic crisis, European leaders and policymakers have recognised that economic and social convergence must go hand in hand if the goals of economic and monetary union are to be achieved. This policy brief provides an updated picture of convergence in employment outcomes across the EU Member States and regions. Five key labour market indicators are examined. The study finds that there has been upward convergence of Member States in most employment indicators for the past two decades. The analysis of regional convergence and convergence in respect of different sociodemographic groups within the population, however, shows less positive developments. The brief also discusses the policy option of implementing a European unemployment insurance scheme for enhancing convergence, or avoiding divergence, within the EU.