The goal of the paper is to show that language can support social and intercultural competence of both students and teachers: one of the ways to do it is teaching cultural taboos and taboo language for intercultural awareness and understanding. The current state of the art in the field points to an increasing interest in the teaching of taboos. The material we analysed consisted in 238 offensive, vulgar and obscene English words that both students and teachers should know to attain social and intercultural competence. The method used is the descriptive one. The degree of novelty is rather high in our cultural area. Results show that there are 134 offensive (slang) words and expressions (referring to the country of origin or to an ethnic group, to sex and sex-related issues (sexual orientation), to race, etc.), 75 vulgar words and expressions (referring to sex and sex-related issues, to body parts, to people, etc.), and 29 obscene words and expressions (referring to body secretions, to sex and sex-related issues, to people, etc.). There seems to be no research limitations given the lexicographic sources that we used. The implications of teaching cultural taboos and taboo language at tertiary level concern both the students and teachers and the organisation they belong to. The paper is original and relevant given the process of globalisation.