In the eukaryotic cell, DNA compaction is achieved through its interaction with histones, constituting a nucleoprotein complex called chromatin. During metazoan evolution, the different structural and functional constraints imposed on the somatic and germinal cell lines led to a unique process of specialization of the sperm nuclear basic proteins (SNBPs) associated with chromatin in male germ cells. SNBPs encompass a heterogeneous group of proteins which, since their discovery in the nineteenth century, have been studied extensively in different organisms. However, the origin and controversial mechanisms driving the evolution of this group of proteins has only recently started to be understood. Here, we analyze in detail the histone hypothesis for the vertical parallel evolution of SNBPs, involving a "vertical" transition from a histone to a protamine-like and finally protamine types (H --> PL --> P), the last one of which is present in the sperm of organisms at the uppermost tips of the phylogenetic tree. In particular, the common ancestry shared by the protamine-like (PL)- and protamine (P)-types with histone H1 is discussed within the context of the diverse structural and functional constraints acting upon these proteins during bilaterian evolution.