Polymer physics is a powerful framework for understanding the physical underpinnings of the spatial organization of eukaryotic chromosomes, including their entanglement when confined inside the nucleus. Theoretical considerations tell us that an equivalent set of long topologically-constrained confined polymers would be strongly entangled once equilibrated. Still, such equilibrium can be reached only over timescales that vastly exceed the lifetime of cells. Long eukaryotic genomes are therefore strongly out of equilibrium, hence their relatively low degree of entanglement that makes possible all DNA transactions in vivo. In this opinion article, Rosa et al. start from these premises and, by reviewing previous studies, argue that a proper account of topological constraints is essential for realistic structural models of eukaryotic genomes. Part of the article’s content reflects discussions held by the authors during Eutopia meetings.