In this concise review we discuss some of the complex edges of the concept of death that arose after the notorious advances in science and medicine over the last 50 years, in which the classical cardio-pulmonary criteria have led to the neurological criteria of death. New complicated questions like the definition of death and the operational criteria for diagnosing it have arisen and we think that they are far from being adequately and satisfactorily solved. A number of important issues -like the reliability and differences between cardio-pulmonary versus brain based criteria of death, if death is an event or a process, the meaning of integration and irreversibility- have not yet received sufficient attention. Here we have approached the death problem from two (biological) complex system perspectives: the organism level and the cellular-molecular level. We also discuss issues from a third systemic approach, that is, the entire society, thus involving legal, religious, bioethical and political aspects of death. Our aim is to integrate new perspectives in order to promote further discussion on these critical yet frequently neglected issues