Higher order chromatin structure, i.e. the three-dimensional (3D) organization of the genome in the interphase nucleus, is an important component in the orchestration of gene expression in the mammalian genome. In this review we describe principles of higher order chromatin structure discussing three organizational parameters, i.e. chromatin folding, chromatin compaction and the nuclear position of the chromatin fibre. We argue that principles of 3D genome organization are probabilistic traits, reflected in a considerable cell-to-cell variation in 3D genome structure. It will be essential to understand how such higher order organizational aspects contribute to genome function to unveil global genome regulation.