This paper is a cross-linguistic study of counterfactuality in simple clauses, as in the English construction The police should have intervened. On the basis of a representative sample of languages, we investigate (i) how counterfactuality is most commonly marked, and (ii) what these patterns of marking can tell us about the nature and origins of counterfactuality. We first show that counterfactuality is most frequently marked by a combination of elements that have other functions in other contexts, rather than by one single ‘dedicated’ marker. Contrary to popular belief, neither past tense nor imperfective aspect is a universal feature in the combinations of markers used to signal counterfactuality: the only type of element that is found in every combination is a modal element marking some type of potentiality, which can be combined (i) with past tense markers, (ii) with a combination of past tense and aspectual (perfect or perfective) markers, or (iii) just with aspectual markers. On the basis of these findings about the marking of counterfactuality, we argue that counterfactuality typically originates as a semanticization of pragmatic information, more specifically an implicature derived from the compositional meaning of a combination of a modal element and a past, perfect or perfective element.