Europe's 2020 strategy and the consequent initiative “Innovation Union” call for a particular attention to the territorial dimension of innovation and knowledge creation. To this end, this paper investigates the nature of knowledge production and diffusion among regions in 29 European Union (EU) countries and tries to assess its effectiveness. Data envelopment analysis is thus applied to assess how efficiently European regions use internal and external inputs for the production of new knowledge and ideas. The analysis produces a ranking of the innovative performance of EU regions for two points in time: the beginning of the current century and the second part of this decade. This ranking is then evaluated through the Malmquist productivity index in order to assess the relative importance of its main components. The Data envelopment analysis provides further evidence of a dualistic (centre versus periphery) pattern in the regional innovation activities, with the most efficient territories located in the most central or economically strategic areas of the continent. The application of the Malmquist productivity index shows that both the magnitude and intrinsic features of the productivity dynamics are extremely differentiated across regions. Again, we observe important differences between the core and periphery of Europe and, more specifically, between the rich and industrialized countries that form the so-called “Old Europe” and the relatively poorer ones that have entered the EU quite recently.