Eukaryotic chromosome replication is mediated by multiple replicons and is coordinated with sister chromatid cohesion, DNA recombination, transcription and cell cycle progression. Replication forks stall or collapse at DNA lesions or problematic genomic regions, and these events have often been associated with recombination and chromosomal rearrangements. Stalled forks generate single-stranded DNA that activates the replication checkpoint, which in turn functions to protect the stability of the fork until the replication can resume. Recombination-mediated and damage-bypass processes are the main mechanisms responsible for replication restart. New findings have helped to unmask the molecular mechanisms that sense replication stress, control the stability of replication forks, and regulate the mechanisms that promote replication restart, thereby giving us a better understanding of how genome integrity is preserved during replication.