The anaphase of mitosis is one of the most critical stages of the cell division cycle in that it can reveal precious information on the fate of a cell lineage. Indeed, most types of nuclear DNA segregation defects visualized during anaphase are manifestations of genomic instability and augur dramatic outcomes, such as cell death or chromosomal aberrations characteristic of cancer cells. Although chromatin bridges and lagging chromatin are always pathological (generating aneuploidy or complex genomic rearrangements), the main subject of this article, the ultrafine anaphase bridges, might, in addition to potentially driving genomic instability, play critical roles for the maintenance of chromosome structure in rapidly proliferating cells.