The duplication of genetic information is central to life. The replication of genetic information is strictly controlled to ensure that each piece of genomic DNA is copied only once during a cell cycle. Factors that slow or stop replication forks cause replication stress. Replication stress is a major source of genome instability in cancer cells. Multiple control mechanisms facilitate the unimpeded fork progression, prevent fork collapse and coordinate fork repair. Chromatin alterations, caused by histone post-translational modifications and chromatin remodeling, have critical roles in normal replication and in avoiding replication stress and its consequences. This text reviews the chromatin regulators that ensure DNA replication and the proper response to replication stress. We also briefly touch on exploiting replication stress in therapeutic strategies. As chromatin regulators are frequently mutated in cancer, manipulating their activity could provide many possibilities for personalized treatment.