Mammalian chromosomes fold into arrays of megabase-sized topologically associating domains (TADs), which are arranged into compartments spanning multiple megabases of genomic DNA. TADs have internal substructures that are often cell type specific, but their higher-order organization remains elusive. Here, we investigate TAD higher-order interactions with Hi-C through neuronal differentiation and show that they form a hierarchy of domains-within-domains (metaTADs) extending across genomic scales up to the range of entire chromosomes. We find that TAD interactions are well captured by tree-like, hierarchical structures irrespective of cell type. metaTAD tree structures correlate with genetic, epigenomic and expression features, and structural tree rearrangements during differentiation are linked to transcriptional state changes. Using polymer modelling, we demonstrate that hierarchical folding promotes efficient chromatin packaging without the loss of contact specificity, highlighting a role far beyond the simple need for packing efficiency.