Understanding how chromatin is organized within the nucleus and how this 3D architecture influences gene regulation, cell fate decisions and evolution are major questions in cell biology. Despite spectacular progress in this field, we still know remarkably little about the mechanisms underlying chromatin structure and how it can be established, reset and maintained. In this Review, we discuss the insights into chromatin architecture that have been gained through recent technological developments in quantitative biology, genomics and cell and molecular biology approaches and explain how these new concepts have been used to address important biological questions in development and disease.