It is very important to know whether someone is alive or dead. Usually, this is obvious, but there are difficult cases such as whole-brain dead patients on life support and brain-injured patients who are in a permanent vegetative state. The traditional way of determining death centered on the cardiorespiratory system: a patient was declared dead when breathing and heartbeat had stopped. Advances in medical technology, including artificial ventilation and resuscitation techniques, brought this connection between death and the cardiorespiratory system into question. In response, “brain death” was proposed. Brain death is a criterion for death that is part of a biological paradigm of death. There are objections to both brain death and the biological paradigm. This has given rise to an alternative consciousness-based paradigm of death. There are objections to this too, which creates a quandary as to what death is and whether it has occurred in difficult cases. Arguably, this quandary was inevitable given the way the ordinary concept of death works. Some responses to this quandary are canvassed, but they are problematic, so the death debate remains unresolved.