Recycling histone proteins from parental chromatin, a process known as parental histone transfer, is an important component in chromosome replication and is essential for epigenetic inheritance. We review recent advances in our understanding of the recycling mechanism of parental histone H3-H4 tetramers (parH3:H4tet), emphasizing the pivotal role of the DNA replisome. In particular, we highlight the function of the MCM2-7 helicase subunit Mcm2 as a histone H3-H4 tetramer chaperone. Disruption of this histone chaperone's functions affects mouse embryonic stem cell differentiation and can lead to embryonic lethality in mice, underscoring the crucial role of the replisome in maintaining epigenomic stability.