Stability and function of eukaryotic genomes are closely linked to chromatin structure and organization. During cell division the entire genome must be accurately replicated and the chromatin landscape reproduced on new DNA. Chromatin and nuclear structure influence where and when DNA replication initiates, whereas the replication process itself disrupts chromatin and challenges established patterns of genome regulation. Specialized replication-coupled mechanisms assemble new DNA into chromatin, but epigenome maintenance is a continuous process taking place throughout the cell cycle. If DNA synthesis is perturbed, cells can suffer loss of both genome and epigenome integrity with severe consequences for the organism.