Abstract The relationship between compartmentalisation of the genome and epigenetics is long and hoary. In 1928 Heitz defined heterochromatin as the largest differentiated chromatin compartment in eukaryotic nuclei. Müller’s (1930) discovery of position-effect variegation (PEV) went on to show that heterochromatin is a cytologically-visible state of heritable (epigenetic) gene repression. Current insights into compartmentalisation have come from a high-throughput top-down approach where contact frequency (Hi-C) maps revealed the presence of compartmental domains that segregate the genome into heterochromatin and euchromatin. It has been argued that the compartmentalisation seen in Hi-C maps is due to the physiochemical process of phase separation. Oddly, the insights provided by these experimental and conceptual advances have remained largely silent on how Hi-C maps and phase separation relate to epigenetics. Addressing this issue directly in mammals, we have made use of a bottom-up approach starting with the hallmarks of constitutive heterochromatin, heterochromatin protein 1 (HP1) and its binding partner the H3K9me2/3 determinant of the histone code. They are key epigenetic regulators in eukaryotes. Both hallmarks are also found outside mammalian constitutive heterochromatin as constituents of larger (0.1-5Mb) heterochromatin -like domains and smaller (less than 100Kb) complexes. The well-documented ability of HP1 proteins to function as bridges between H3K9me2/3-marked nucleosomes enables cross-linking within and between chromatin fibres that contributes to polymer-polymer phase separation (PPPS) that packages epigenetically-heritable chromatin states during interphase. Contacts mediated by HP1 “bridging” are likely to have been detected in Hi-C maps, as evidenced by the B4 heterochromatic sub-compartment that emerges from contacts between large KRAB-ZNF heterochromatin -like domains. Further, mutational analyses have revealed a finer, innate, compartmentalisation in Hi-C experiments that likely reflect contacts involving smaller domains/complexes. Proteins that bridge (modified) DNA and histones in nucleosomal fibres – where the HP1-H3K9me2/3 interaction represents the most evolutionarily-conserved paradigm – could drive and generate the fundamental compartmentalisation of the interphase nucleus. This has implications for the mechanism(s) that maintains cellular identity, be it a terminally-differentiated fibroblast or a pluripotent embryonic stem cell.