This study uses Data Envelopment Analysis to analyse the evolution of the efficiency of the European Union banking sector with different concepts and measures of bank efficiency, as well as the results provided by the Malmquist index to measure different efficiency changes, and the total productivity changes considering a panel of 784 relevant banks from all the 27 European Union countries, between 2006 and 2021. Banks are assumed to produce three outputs: loans, other earning assets, and non-earning assets using three inputs: interest expenses, non-interest expenses, and equity, overall, the findings of the paper point to the existence of inefficiencies which are mainly justified by non-optimal combinations of the considered inputs and outputs, and not by the scale of the production. The results obtained also reveal that the EU banks included in the sample have room to improve their choices of the combinations of inputs to produce the desired outputs at minimum costs. The values of the computed Malmquist index indicate overall progress, except during the period of the global financial crisis, and to some extent also between the years 2015-2017, corresponding to a turbulent period of the EU banking sector with the advancements of the European Banking Union and two relevant initiatives: the European Banking Supervision and the Single Resolution Mechanism.