This introductory article to the inaugural issue of Migration and Society reflects on the complex and often contradictory nature of migration encounters by focusing on diverse dynamics of hospitality and hostility towards migrants around the world and in different historical contexts. Discourses, practices, and policies of hospitality and hostility towards migrants and refugees raise urgent moral, ethical, political, and social questions. Hospitality and hostility are interlinked, yet seemingly contradictory concepts and processes, as also acknowledged by earlier writers, including Derrida, who coined the term hostipitality. Drawing on Fiddian-Qasmiyeh’s work and on feminist scholars of care, we argue for the need to trace alternative modes of thought and action that transcend and resist the fatalistic invocations of hostipitality. This requires an unpacking of the categories of host and guest, taking us from universalizing claims and the taxonomy of host-guest relations to the messiness of everyday life and its potential for care, generosity, and recognition in encounters.