Advancements in biotechnologies invite the hope for the eradication of the natural causes of death. Some people welcome this possibility, foreseeing a bright future finally free from those pain and evils which have been historically afflicting humanity; others believe that in this way the human species will eventually disappear. The purpose of this essay is to show that these two alternatives are too radical. Society and human culture are direct consequences of human mortality: eliminating mortality will produce consequences that we are not able to fully anticipate. Some writers have given us indications of what a future populated with immortals might look like, which is far removed both from the bright future painted by the Transumanists and from the disappearance of humanity feared by bioconservatives.