Caring for extremely premature babies is difficult and costly. Mortality has been reduced with recent medical progress, but at the price of an increased number of surviving infants with handicaps. Should we then fix firm limits (gestational age and/or birthweight) for deciding on whether or not to take medical action? There is however the question of whether it is ethically acceptable to define human life solely on the basis of the length of gestation or birthweight. Moreover, what risk level for death or handicap is legitimate for treating or not a premature baby? The issue thus comes to the worthiness of trying first to save life, then accepting an interruption of curative treatments later on if severe cerebral injuries become evident. Who should make the decisions? Guidelines have been published by medical associations to help professionals to answer these important and puzzling questions.