In this article, we analyze contradictions, complexities, limits, and potentialities of internationalization of higher education (IHE) from Latin American decolonial perspectives. We argue that even when scholars may be holding decolonial critiques and aspirations towards IHE, the structures of universities are heavily influenced by colonial legacies, undermining the potentialities of decolonization. We pay special attention to those initiatives that apparently promise a decolonial exit, because they may be acting as traps, or what we called trampas (in Spanish). In this article, we particularly analyze the initiatives that are frequently seen as projects that deviated from the hegemonic discourses of internationalization: i) South-South international higher education cooperation projects, ii) policies and projects that seek to address colonial legacies, and iii) teaching and researching committed with decolonial intentions. In the end, we invite readers, practitioners and scholars alike, to welcome the contradictions we face in such work and not to lose sight of the ongoing, relational, and hyperreflective character of any project that aims to be an alternative to coloniality.