This chapter considers whether life extension per se can be an aim of medicine. It first provides an initial tentative analysis of what it means for something to be an aim or goal of medicine in general and whether there are any normative restrictions on what can be an aim or goal of medicine. It then applies this analysis to moderate and radical life extension. It is concluded that moderate life extension has many affinities with other aims and goals that are accepted as uncontroversial goals of medicine and that there are no conclusive arguments showing that it falls outside the scope of proper medicine. It is further concluded that radical life extension falls outside the current scope of medicine and that medicine as a normative practice would have to be significantly reconfigured if radical life extension is to become an aim of medicine.