Europe 2020 strategy and the initiative “Innovation Union” call for a particular attention at the territorial dimension of innovation and knowledge creation. The heterogeneity across regions in their capacity to create knowledge and innovation, but also in their abilities to exploit ideas and technologies available across the European territory, motivates in-depth analyses of the territorial dimension of the knowledge economy. This paper investigates the nature of knowledge production and diffusion among regions in 29 EU countries and tries to assess its effectiveness. The analysis follows a two-step analytical route. Firstly, as a preliminary analysis, we estimate a knowledge production function (Griliches, 1979 and many others) with the usual parametric methods, in order to find out which are the main determinants of knowledge production at the regional level in Europe. Secondly, based on these findings, we apply DEA to assess the degree of efficiency of European regions in their use of internal and external inputs for the production of new knowledge and ideas. This allows to provide 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. Such rankings will be evaluated thanks to the Malmquist productivity index in order to assess the relative importance of its main components. According to the Data Envelopment Analysis, we found further evidence of a dualistic (centre vs periphery) pattern in the regional innovation activities, with the highest efficient territories located in the most central or economically strategic areas of the continent. On the contrary, the application of the Malmquist productivity index shows that productivity dynamics has been extremely differentiated across regions in terms of both magnitude and intrinsic features. We, again, observe important differences between the core and periphery of Europe and most specifically between the countries which are rich and industrialized and form the so called “Old Europe” and those which are relatively poor and have entered the European Union quite recently.