We analyze four interrelated aspects of economic convergence and their linkages over the period 1999-2013, drawing on the experiences of 26 member states of the European Union, with special focus on the ten Central and East-European new members (the EU10). These aspects are (1) real economic, (2) price level, (3) structural and (4) wage level convergence. Real economic and price level convergence, respectively, refer to the narrowing of the income (productivity) and the price level gap between the more and less affluent countries. Regarding structural convergence, we focus on the evolution of the share and the relative price of private and public services, measured from the expenditure side. As for wage convergence, we address the catching up of nominal and real labor costs, as well as net earnings of the poorer countries to the more developed ones. Our empirical analysis of convergence draws on both the cross-section and the dynamic relationships revealed by the data. Regarding real and price convergence, we show that there was a rapid catch-up in both per capita GDPs and general price levels of the less developed EU-countries until 2008, followed by a significant slow-down. We also show that there is a tendency for price levels to converge towards the trend implied by the longer-term relationship between real per capita GDPs and price levels. Our research affirms and amends the finding that positive/negative deviations from the trend ("over/undervaluations") have a negative/positive effect on real economic convergence. Relying on cross-country price level indices (PLIs), we demonstrate that the relative price of services does, but their "real" share (measured at common prices of the EU) does not increase along with real income. We show that this is mainly due to the fact that non-market services (in particular government transfers in kind) have a relatively high, though slowly declining real share in the less developed EU countries, which also helps us understand, why net real wages are relatively low in these countries (as compared to their relative level of income/productivity). We construct a model, which is consistent with developments in the EU10. Our findings relate to factors affecting real economic convergence, the ambiguous relationship between economic development and the change in the real share of services, to real exchange rate misalignments within the EU26, and reflect to the notion of "excessively low wages" in the EU10 countries.