This paper investigates the emergence of polarisation patterns in the EU during the last 60 years from a structuralist and complexity economics perspective. Based on the results, feasible opportunities for EU policy-making, which aim to counteract a tendency of polarization, are delineated. The study comprises of a historical analysis of the politico-economic events during this time and a complementary quantitative analysis of the European trade network. The results suggest that trade in the Eurozone is unequal at the expense of the peripheries and follows a pattern of "unequal technological exchange". The paper also assesses the usefulness of country taxonomies such as 'cores' and 'peripheries' for identifying the roots of polarization patterns. While it generally affirms the relevance of structural dependencies, and confirms the epistemic usefulness of country taxonomies, it also highlights three challenges - the challenges of dynamics, of ambiguity and granularity - that any such taxonomy necessarily faces, and which must be dealt with explicitly in any structuralist analysis using such taxonomies.