This book describes the most outstanding theoretical hypotheses aiming at explaining the infinite proliferative potential of a cell population, what is now known under the term cell immortalization. It elucidates the phenomenon from an evolutionary point of view, and describes the cell systems used and the experiments performed at the cellular and molecular levels to determine the mechanisms responsible for this cell property. It also appraises how the mortal and immortal phenotypes reflect characteristics of the respective organism, and stresses how this goes beyond the proposal that its opposite, the mortal phenotype, is a mechanism to protect the organism against cancer.