Since the discovery of chromosome territories, it has been clear that DNA within the nucleus is spatially organized. During the last decade, a tremendous body of work has described architectural features of chromatin at different spatial scales, such as A/B compartments, topologically associating domains (TADs), and chromatin loops. These features correlate with domains of chromatin marking and gene expression, supporting their relevance for gene regulation. Recent work has highlighted the dynamic nature of spatial folding and investigated mechanisms of their formation. Here we discuss current understanding and highlight key open questions in chromosome organization in animals.