Replicative senescence is an essential cellular process playing important physiological functions, but it is better known for its implications in aging, cancer, and other pathologies. One of the main triggers of replicative senescence is telomere shortening and/or its dysfunction and, therefore, a deep understanding of the molecular determinants is crucial. However, replicative senescence is a heterogeneous and hard to study process, especially in mammalian cells, and some important questions still need an answer. These questions concern i) the exact molecular causes triggering replicative senescence, ii) the role of DNA repair mechanisms and iii) the importance of R-loops at telomeres in regulating senescence onset, and iv) the mechanisms underlying the bypass of replicative senescence. In this review, we will report and discuss recent findings about these mechanisms both in mammalian cells and in the model organism Saccharomyces cerevisiae.