In eukaryotes, telomeres cap chromosome ends to maintain genomic stability. Failure to maintain telomeres leads to their progressive erosion and eventually triggers replicative senescence, a pathway that protects against unrestricted cell proliferation. However, the mechanisms underlying the variability and dynamics of this pathway are still elusive. Here we use a microfluidics-based live-cell imaging assay to investigate replicative senescence in individual Saccharomyces cerevisiae cell lineages following telomerase inactivation. We characterize two mechanistically distinct routes to senescence. Most lineages undergo an abrupt and irreversible switch from a replicative to an arrested state, consistent with telomeres reaching a critically short length. In contrast, other lineages experience frequent and stochastic reversible arrests, consistent with the repair of accidental telomere damage by Pol32, a subunit of polymerase δ required for break-induced replication and for post-senescence survival. Thus, at the single-cell level, replicative senescence comprises both deterministic cell fates and chaotic cell division dynamics.