During the cell cycle, the genome must undergo dramatic changes in structure, from a decondensed, yet highly organized interphase structure to a condensed, generic mitotic chromosome and then back again. For faithful cell division, the genome must be replicated and chromosomes and sister chromatids physically segregated from one another. Throughout these processes, there is feedback and tension between the information-storing role and the physical properties of chromosomes. With a combination of recent techniques in fluorescence microscopy, chromosome conformation capture (Hi-C), biophysical experiments, and computational modeling, we can now attribute mechanisms to many long-observed features of chromosome structure changes during cell division. Apparent conflicts that arise when integrating the concepts from these different proposed mechanisms emphasize that orchestrating chromosome organization during cell division requires a complex system of factors rather than a simple pathway. Cell division is both essential for and threatening to proper genome organization. As interphase three-dimensional (3D) genome structure is quite static at a global level, cell division provides an important window of opportunity to make substantial changes in 3D genome organization in daughter cells, allowing for proper differentiation and development. Mistakes in the process of chromosome condensation or rebuilding the structure after mitosis can lead to diseases such as cancer, premature aging, and neurodegeneration. WIREs Syst Biol Med 2017, 9:e1389. doi: 10.1002/wsbm.1389 For further resources related to this article, please visit the WIREs website.