In eukaryotes, the genome does not exist as a linear molecule but instead is hierarchically packaged inside the nucleus. This complex genome organization includes multiscale structural units of chromosome territories, compartments, topologically associating domains, which are often demarcated by architectural proteins such as CTCF and cohesin, and chromatin loops. The 3D organization of chromatin modulates biological processes such as transcription, DNA replication, cell division and meiosis, which are crucial for cell differentiation and animal development. In this Review, we discuss recent progress in our understanding of the general principles of chromatin folding, its regulation and its functions in mammalian development. Specifically, we discuss the dynamics of 3D chromatin and genome organization during gametogenesis, embryonic development, lineage commitment and stem cell differentiation, and focus on the functions of chromatin architecture in transcription regulation. Finally, we discuss the role of 3D genome alterations in the aetiology of developmental disorders and human diseases.