Condensins and cohesins are highly conserved complexes that tether together DNA loci within a single DNA molecule to produce DNA loops. Condensin and cohesin structures, however, are different, and the DNA loops produced by each underlie distinct cell processes. Condensin rods compact chromosomes during mitosis, with condensin I and II complexes producing spatially defined and nested looping in metazoan cells. Structurally adaptive cohesin rings produce loops, which organize the genome during interphase. Cohesin-mediated loops, termed topologically associating domains or TADs, antagonize the formation of epigenetically defined but untethered DNA volumes, termed compartments. While condensin complexes formed through cis-interactions must maintain chromatin compaction throughout mitosis, cohesins remain highly dynamic during interphase to allow for transcription-mediated responses to external cues and the execution of developmental programs. Here, I review differences in condensin and cohesin structures, and highlight recent advances regarding the intramolecular or cis-based tetherings through which condensins compact DNA during mitosis and cohesins organize the genome during interphase. © 2019. Published by The Company of Biologists Ltd.