There has not been much progress on the poverty front in Europe over recent decades, at least if we take it as a relative phenomenon in affluent societies. There is a lot of pessimism about the possibility of making any real progress at all. Some argue that adequate poverty relief is simply too expensive or that it would put too much of a redistributive burden on the electorally powerful, making it politically difficult, if not infeasible. Another prominent argument is that wage floors and thus out-of-work benefit levels are inexorably under pressure, making poverty relief both harder to achieve and more expensive in budgetary terms. This paper sets out these accounts and focuses on what has been happening to statutory, absolute and effective wage floors in Europe over the past decades. We ask whether progress on the poverty front through pushing up wage floors and subsequently out-of-work benefits is a realistic prospect. We see reasons for optimism.