Exchange rate assessment is becoming increasingly relevant for economic surveillance in the EU. The persistence of different wage and productivity dynamics among EMU countries or EU members with a fixed exchange regime with euro, coupled with the impossibility of correcting competitiveness differentials via the adjustment of nominal rates, have resulted into divergent dynamics in Real Effective Exchange Rates. This paper explores the role of economic fundamentals in explaining medium/long-run movements in the Real Effective Exchange Rates in the European Union over the period 1994-2012 by using heterogeneous, cointegrated panel frameworks in static and dynamic terms. In addition, the paper provides an analysis of the misalignments of the rate for each member state based on the "equilibrium" measure calculated from the permanent component of the fundamentals (BEER). The misalignments in EU28 are huge and the patterns differ significantly among groups. Therefore, despite the influence of the fundamentals is quite similar, the differences in the transfer variable (which affect the BEER) and in the actual Real Effective Exchange Rate are key. The core countries have been undervalued for almost the whole period, which entails from an important increase in competitiveness for those countries. Instead the periphery has experienced high rates, especially in Portugal. In addition, the behavior of CEECs is driven, as expected, by the transition process and influenced by the criteria to the accession to the EU. The misalignments in this case are still extremely wide and reflect these phenomena.