European countries have the world's most redistributive tax and transfer systems. While they have been well equipped to deal with vertical inequality fostering redistribution from the rich to the poor - less is known about their performance in dealing with horizontal inequality, that is, in redistributing across socioeconomic groups. In a context where individuals may not only care about vertical redistribution, but also about the economic situation of the specific groups they belong to, the horizontal dimension of redistribution becomes politically salient and can be a source of social tensions. The authors analyse the performance of the 28 EU countries for redistribution across (i) age groups; (ii) occupational groups; and (iii) household types over the period 2007-2014 using counterfactual simulation techniques. We find a significant degree of heterogeneity across countries: changes in the tax and transfer system have particularly hit the young and the losers of occupational change in Eastern European countries, while households with greater economic security have benefited from these changes. The findings of this study suggest that horizontal inequality is a dimension which policy-makers should take into account when reforming tax and transfer systems.