S phase is a period of great vulnerability for the genome of eukaryotic cells. Many complicated processes are undertaken during this critical phase of the cell cycle, including the complete unwinding and the duplication of enormously complex DNA molecules. During this process, replication forks frequently encounter obstacles that impede their progression. Arrested forks are unstable structures that have to be stabilized and restarted in order to prevent the formation of double-strand breaks and/or unscheduled homologous recombination. To this aim, cells have evolved complex surveillance mechanisms sensing DNA damage and replication stress. The past decade has seen a dramatic advance in our understanding of how these regulatory pathways act in response to exogenous replication stress. However, the mechanism by which fork integrity is maintained at natural replication-impeding sequences remains obscure. Here, we discuss recent findings about how checkpoint-dependent and -independent mechanisms cooperate to prevent genomic instability at stalled forks, both in normal S phase and in the presence of exogenous genotoxic stress.