There has been growing concern about whether individuals who satisfy neurological criteria for death or who become non-heart-beating organ donors are really dead. This concern has focused on the issue of the potential for recovery that these individuals may still have and whether their conditions are irreversible. In this article I examine the concepts of potentiality and irreversibility that have been invoked in the discussions of the definition of death and non-heart-beating organ donation. I initially focus on the recent challenge by D. Alan Shewmon to accepting any neurological criterion of death. I argue that Shewmon relies on a problematic and unrealistic concept of potentiality, and that a better, more realistic concept of potentiality is consistent with accepting a neurological criterion for death. I then turn to an analysis of how the concept of irreversibility has been used in discussion of non-heart-beating organ donation. Similarly, I argue that some participants in this discussion have invoked a problematic and unrealistic concept of irreversibility. I then propose an alternative, more realistic account of irreversibility that explains how "irreversibility" should be understood in the definition and criteria of death.