Using harmonised data from the European Union Household Panel, we analyse gender pay gaps by sector across the wages distribution for ten countries. We find that the mean gender pay gap in the raw data typically hides large variations in the gap across the wages distribution. We use quantile regression (QR) techniques to control for the effects of individual and job characteristics at different points of the distribution, and calculate the part of the gap attributable to differing returns between men and women. We find that, first, gender pay gaps are typically bigger at the top of the wage distribution, a finding that is consistent with the existence of glass ceilings. For some countries gender pay gaps are also bigger at the bottom of the wage distribution, a finding that is consistent with sticky floors. Third, the gender pay gap is typically higher at the top than the bottom end of the wage distribution, suggesting that glass ceilings are more prevalent than sticky floors and that these prevail in the majority of our countries. Fourth, the gender pay gap differs significantly across the public and the private sector wages distribution for each of our EU countries.