Popper's falsifiability criterion of demarcation is critically examined, both as a proposal with an independent epistemological rationale and as a condition which modern science is supposed to satisfy, and some famous objections to it are discussed. While possessing an irresistible epistemological appeal, an analysis of the objections arising from the Duhem problem shows that there is an immediate conflict, and not a mutual support, between Popper's methodological approach to falsifiablity in Logik der Forschung and his formal criterion of demarcation. Moreover, and partly owing to this unnoticed conflict, his classic defence of falsi-ficationism as an alternative to conventionalism is shown to rely on assumptions linking testability with meaning which, contrary to what is sometimes supposed, were shared by Popper with some of his positivist and conventionalist targets, and later superseded by his realist and objectivist conception of scientific statements.