Recent systematic studies using newly developed genomic approaches have revealed common mechanisms and principles that underpin the spatial organization of eukaryotic genomes and allow them to respond and adapt to diverse functional demands. Genomes harbor, interpret, and propagate genetic and epigenetic information, and the three‐dimensional (3D) organization of genomes in the nucleus should be intrinsically linked to their biological functions. However, our understanding of the mechanisms underlying both the topological organization of genomes and the various nuclear processes is still largely (...) incomplete. In this essay, we focus on the functional relevance as well as the biophysical properties of common organizational themes in genomes (e.g. looping, clustering, compartmentalization, and dynamics), and examine the interconnection between genome structure and function from this angle. Present evidence supports the idea that, in general, genome architecture reflects and influences genome function, and is relatively stable. However, the answer as to whether genome architecture is a hallmark of cell identity remains elusive. (shrink)