Normal somatic cells loose the ability to divide after a limited number of cell divisions. This phenomenon, known as replicative senescence, is an important barrier to tumor progression. Essentially all human cancers acquire mechanisms that allow them to escape replicative senescence, most often through high levels of telomerase expression (∼ 90%). In this talk we will discuss how replicative senescence can protect against early non-neoplastic mutations that are potentially cancer precursors. We will also discuss various mathematical approaches to calculate the probability of escaping replicative senescence through a mutation that activates telomerase.