The maintenance of the genome during replication requires the assembly of nucleosomes with newly synthesized histones. Achieving the deposition of newly synthesized histones in chromatin implies their transport from the cytoplasm to the nucleus at the replication sites. Several lines of evidence have revealed critical functions of the histone tail domains in these conserved cellular processes. In this review, we discuss the role of the amino termini of the nucleosome building blocks, H2A/H2B and H3/H4, in different model systems. The experimental data showed that H2A/H2B tails and H3/H4 tails display distinct functions in nuclear import and chromatin assembly. Furthermore, we describe recent studies exploiting the unique properties of the slime mold, Physarum polycephalum , that have advanced understanding of the function of the highly conserved replication-dependent diacetylation of H4.