What happens to human-computer "interaction" when the human user is no longer alive? This exploratory paper uses insights from the critical humanist tradition to argue for the urgent need to consider the facts of mortality, dying, and death in HCI research. Using an interdisciplinary approach, we critically reflect upon how the intersection of death and computing is currently navigated and illustrate the conceptual and practical complexities presented by mortality, dying, and death in HCI. Finally, we introduce the concept of thanatosensitivity to describe an approach that actively integrates the facts of mortality, dying, and death into HCI research and design. Keywords Death, dying, mortality, critical humanism, thanatosensitivity. ACM Classification Keywords H5.m. Information interfaces and presentation (e.g., HCI): Miscellaneous.