Attaining a mastery of understanding and using a foreign language includes the ability of grasping the implied meaning of the text, i.e. comprehending the speaker's / author's communicative intention. In this respect, grasping the nuances of humour and irony is one of the most difficult aspects of foreign language acquisition, requiring pragmatic, discursive and sociocultural competences. These interrelated competences testify to the learner's language proficiency. Our research deals with humour and irony in political discourse and is based on political jokes and authentic political texts which are used as reading material in contemporary language teaching. The study of humour as a rhetorical device in political speeches has attracted considerable attention of scholars in interdisciplinary research and shows that both political discourse and humour have culture-specific features which should be taken into consideration. Ignoring culturally bound differences related to humour and irony in political discourse can lead to dramatic and unfortunate consequences (the tragedy in Charlie Hebdo in 2015 is a vivid example). The present paper focuses on modern British and American political discourse and explores the role of irony in the speeches of politicians. Drawing on critical discourse analysis and constructivist approach, we offer a methodology of teaching how best to understand and interpret irony in a foreign language classroom. Our methodology is aimed at involving the students in discourse analysis and interactive activities to enable them to become reflective and critical thinkers. The results of the study can be applied in second language learning as well as in educating public speakers.