The digital economy is increasingly seen as an essential cornerstone in developing national strategies and industrial policies to enhance national competitiveness. On the other hand, a realistic assessment of digital readiness is essential for developing appropriate policies. In our paper, we group the countries of the European Union (EU) using three different methods applied to a dataset consisting of the four main dimensions of the EU's Digital Economy and Society Index (DESI) in order to identify Europe's main geographical “fault lines” in terms of digital readiness. DESI is a composite index aggregating several digitalization-related indicators to benchmark the progress of digital transformation in each member state. However, our methods aim not to rank countries but to identify groups of countries that are close to each other. The three methods used in the paper are partially ordered sets (poset), Tiered Data Envelopment Analysis (TDEA), and cluster analysis, known from multivariate statistics. The three types of clustering show a high degree of similarity, indicating the robustness of the results. Another research question relates to the extent to which the digital development of the EU Member States corresponds to the economic development of the countries and core–periphery relationships. While we can observe a high degree of similarity between the more and less developed clusters in terms of digital readiness and the groups that can be identified in terms of economic development and institutional quality, we also notice some peculiar exceptions (which could provide examples of best practices).