In lively on-going debates among philosophers of science, it is customary to distinguish four main approaches to scientific progress: epistemic (progress as increasing knowledge), semantic (increasing truthlikeness), functional (increasing effectiveness in problem-solving), and noetic (increasing understanding). This chapter formulates the relevant philosophical problem of defining scientific progress, outlines the historical roots of the debate, summarises the basic ideas in the explication of the notion of truthlikeness or verisimilitude after Karl Popper’s pioneering but unsuccessful attempt to characterise ‘closeness to the truth’, and defends the semantic account against its main rivals. It is argued that the semantic account is more adequate and fundamental than its alternatives.