During DNA replication, nucleosomes ahead of replication forks are disassembled to accommodate replication machinery. Following DNA replication, nucleosomes are then reassembled onto replicated DNA using both parental and newly synthesized histones. This process, termed DNA replication-coupled nucleosome assembly (RCNA), is critical for maintaining genome integrity and for the propagation of epigenetic information, dysfunctions of which have been implicated in cancers and aging. In recent years, it has been shown that RCNA is carefully orchestrated by a series of histone modifications, histone chaperones and histone-modifying enzymes. Interestingly, many features of RCNA are also found in processes involving DNA replication-independent nucleosome assembly like histone exchange and gene transcription. In yeast, histone H3 lysine K56 acetylation (H3K56ac) is found in newly synthesized histone H3 and is critical for proper nucleosome assembly and for maintaining genomic stability. The histone acetyltransferase (HAT) regulator of Ty1 transposition 109 (Rtt109) is the sole enzyme responsible for H3K56ac in yeast. Much research has centered on this particular histone modification and histone-modifying enzyme. This Critical Review summarizes much of our current understanding of nucleosome assembly and highlights many important insights learned from studying Rtt109 HATs in fungi. We highlight some seminal features in nucleosome assembly conserved in mammalian systems and describe some of the lingering questions in the field. Further studying fungal and mammalian chromatin assembly may have important public health implications, including deeper understandings of human cancers and aging as well as the pursuit of novel anti-fungal therapies.