We consider and attempt to understand the gender wage gap across 24 EU member states, all of which share the objective of gender equality, using 2007 data from the European Union Statistics on Income and Living Conditions. The size of the gender wage gap varies considerably across countries and selection corrections affect the offered gap, sometimes substantially. Most of the gap cannot be explained by the characteristics available in this data set. Quantile regressions show that, in most countries, the wage gap is wider at the top of the wage distribution ('glass ceilings') and, in fewer countries, it is wider at the bottom of the wage distribution ('sticky floors'). These features are related to country-specific characteristics that cannot be evaluated at the member state level. We use the cross-country variation in this large sample of member states to explore the influence of (i) policies concerned with reconciling work and family life and (ii) wage-setting institutions. We find that policies and institutions are systematically related to unexplained gender wage gaps.