This article uses self-organizing maps (SOMs) to examine convergence between European states, giving special attention to the states of Central and Eastern Europe (CEE) that joined the European Union (EU) during its monumental expansion in 2004. To augment the literature on income convergence, the robust conceptual framework employed here is based upon Terry Jordan’s much broader socioeconomic and political definition of Europe. Using associated variables, the study applies the Kohonen data visualization technique to highlight statistical clustering and movement of countries across three time periods from 2001 to 2013. Kohonen U-matrix and component maps reveal several distinct clusters of countries that remain stable over time, including Europe’s industrialized core and Scandinavia, as well as a cluster of laggard Soviet successor states at the opposite extreme. The eleven new EU countries that had been part of the eastern bloc show evidence of real (β-) convergence toward the European core, but at various paces. The Baltic states of Lithuania and Latvia experience some of the greatest observable convergence, followed by Estonia, the Visegrád states, and the former Yugoslav states of Croatia and Slovenia. Other countries that demonstrate considerable movement during the time period under investigation include some crisis-battered Mediterranean countries, plus Montenegro, Kosovo, and Turkey. While most of the evident statistical mobility is positive, Ireland experiences nominal and real divergence during the period 2011–13. In the context of Europe’s ongoing recession and the aftermath of the UK’s referendum, these findings have implications for two uncertainties: the very survival of the EU and its prospects for further expansion.