In eukaryotic cells, most of the genetic material is contained within a highly specialized organelle—the nucleus. A large body of evidence indicates that, within the nucleus, chromatinized DNA is spatially organized at multiple length scales. The higher-order organization of chromatin is crucial for proper execution of multiple genome functions, including DNA replication and transcription. Here, we review our current knowledge on the spatial organization of chromatin in the nucleus of mammalian cells, focusing in particular on how chromatin is radially arranged with respect to the nuclear lamina. We then discuss the possible mechanisms by which the radial organization of chromatin in the cell nucleus is established. Lastly, we propose a unifying model of nuclear spatial organization, and suggest novel approaches to test it.