The replication-stress response enables the DNA replication machinery to overcome DNA lesions or intrinsic replication-fork obstacles, and it is essential to ensure faithful transmission of genetic information to daughter cells. Multiple replication stress–response pathways have been identified in recent years, thus raising questions about the specific and possibly redundant functions of these pathways. Here, we review the emerging mechanisms of the replication-stress response in mammalian cells and consider how they may influence the dynamics of the core DNA replication complex.