Since its inception, the European Parliament (EP) has experienced an almost parallel rise in the share of elected women and in the number of member states mandating gender quotas at the party list level. Building upon the ``critical mass'' framework, we provide the first comprehensive assessment of the effect of quotas on women's descriptive and substantive representation in the EP. We find that quotas, while (mechanically) raising the number of women running for the EP, left the share of elected women unaffected. The policy, in fact, did not boost voters' likelihood to vote for women, while making party selectorates more likely to relegate female candidates to the bottom of the electoral lists. Although quotas did not increase women's descriptive representation in the EP, they appear to have made male MEPs more `disciplined' in Roll Call Votes. This effect is not driven by a change in the average educational attainments nor in the distribution of leadership roles within the EP. Rather, we show that quotas, reducing the slots available to men in party lists, worsened their re-electability perspectives.