The nucleosomal organization of eukaryotic chromatin is generally established during DNA replication by the deposition of canonical histones synthesized in S phase. However, cells also use a Replication Independent (RI) nucleosome assembly pathway that allows the incorporation of non-canonical histone variants in the chromatin. H3.3 is a conserved histone variant that is structurally very close to its canonical counterpart but nevertheless possesses specific properties. In this review, we discuss the dual role of H3.3 which functions as a neutral replacement histone, but also participates in the epigenetic transmission of active chromatin states. These properties of H3.3 are also explored in the light of recent studies that implicate this histone and its associated chromatin assembly factors in large scale, replication-independent chromatin remodeling events. In particular, H3.3 appears as a critical player in the transmission of the paternal genome, from sperm to zygote.