Humourists often resort to previous texts to create their jokes, thus establishing intertextual links between them. Consequently, the processing of such jokes presupposes specific cultural literacy skills which enable speakers to recognise the allusions and interpret them in the new humorous contexts. It has, however, been suggested that speakers’ emphasis on cultural literacy skills for processing allusions and humour may discourage or even impede them from adopting a critical perspective on humorous texts and the allusions included therein. The present study explores this interplay among intertextuality, cultural literacy, critical literacy, and humour in order to underscore the need for critical approaches to humorous texts and intertextuality. It critically analyses political jokes to demonstrate how the intertextual references contributing to their humorous effect create three sets of opposing groups: (a) those who create/tell the jokes vs. those who are targeted by them; (b) the ‘culturally literate’ who employ and understand the intertextual references vs. the ‘culturally illiterate’ who cannot and/or do not do that; and (c) those who agree vs. those who disagree with the ideological presuppositions of the humorous allusions and texts at hand. Based on incongruity and superiority theories of humour, the proposed analysis intends to argue, and pave the way, for more critical perspectives on humorous genres, whether outside or inside educational settings. Such perspectives could sensitise speakers to the fact that humour and intertextuality divide them into opposing groups such as the above-mentioned ones.