The patterns of the large-scale spatial organization of chromatin in interphase human somatic cells are not random. Such patterns include the radial separation of euchromatin and heterochromatin, the territorial organization of individual chromosomes, the non-random locations of chromosome territories and the differential positioning of the two X chromosomes in female cells. These features of large-scale nuclear architecture follow naturally from the hypothesis that ATP-consuming non-equilibrium processes associated with highly transcribed regions of chromosomes are a source of ‘active’ forces. These forces are in excess of those that arise from Brownian motion. Simulations of model chromosomes that incorporate such activity recapitulate these features. In addition, they reproduce many other aspects of the spatial organization of chromatin at large scales that are known from experiments. Our results, reviewed here, suggest that the distribution of transcriptional activity across chromosomes underlies many aspects of large-scale nuclear architecture that were hitherto believed to be unrelated.