In this conceptual article, we problematize current models of intercultural competence, by tracing the development of models of communicative competence and their historical rootedness in notions of communication as a linguistic phenomenon that occurs primarily in face-to-face encounters. We argue for a view of interculturality that sees intercultural encounters as meaning design processes that can also occur in encounters with texts expressed through multimodal semiotic resources. Finally, we propose a set of principles for second/foreign language education that focus on students' process of becoming effective intercultural interpreters and meaning designers rather than solely on being effective intercultural speakers.