As higher education is increasingly called upon to play a central role in addressing the challenges and crises of today's complex, uncertain, and volatile world, internationalization efforts are intensifying. Emphasizing higher education as a space for critically-informed, socially accountable, and open-ended conversations about alternative futures, in this paper I reframe common approaches to complexity, uncertainty, and critique by offering a social cartography of three critical approaches to internationalization: soft, radical, and liminal. Mapping and historicizing diverse perspectives can complicate existing analyses, interrupt the prescriptive tendencies of critique, and illuminate new possible horizons of thought and action in higher education.