Whilst not all irony (understood as a figure of speech) coincides with humour, the two phenomena do overlap. The paramount objective of this paper is to elucidate the central factors which render irony humorous, on the strength of incongruity and superiority theories of humour, as well as several cognitive and pragmatic postulates on irony put forward outside humour studies. To meet this goal, the present paper takes as its departure point a neo-Gricean view on irony, in the light of which its four types are distinguished (propositional negation irony, ideational reversal irony, verisimilar irony, and surrealistic irony). The incongruity-resolution model, representing the hearer’s inferential process, is shown to operate in the four types of irony discerned, in accordance with the four major cognitive rules. Additionally, several distinctive features of humorous irony are addressed. Finally, the superiority theory, it is argued, can be grafted on the incongruity-resolution theory whenever sarcastic irony is involved.