DNA replication is a highly conserved process that accurately copies the genetic information from one generation to the next. The processes of chromatin disassembly and reassembly during DNA replication also have to be precisely regulated to ensure that the genetic material is compactly packaged to fit into the nucleus while also maintaining the epigenetic information that is carried by the histone proteins bound to the DNA, through cell divisions. Half of the histones that are deposited during replication are from the parental chromatin and carry the parental epigenetic information, while the other half of the histones are newly-synthesized. It has been of growing interest to understand how the parental pattern of epigenetic marks is re-established on the newly-synthesized histones, in a DNA sequence-specific manner, in order to maintain the epigenetic information through cell divisions. In this review we will discuss how histone chaperone proteins precisely coordinate the chromatin assembly process during DNA replication. We also discuss the recent evidence that histone-modifying enzymes, rather than the parental histones, are themselves epigenetic factors that remain associated with the DNA through replication to re-establish the epigenetic information on the newly-assembled chromatin.