The eukaryotic cell cycle is conventionally viewed as comprising several discrete steps, each of which must be completed before the next one is initiated. However, emerging evidence suggests that incompletely replicated, or unresolved, chromosomes from S-phase can persist into mitosis, where they present a potential threat to the faithful segregation of sister chromatids. In this review, we provide an overview of the different classes of loci where this 'unfinished S-phase business' can lead to a variety of cytogenetically distinct DNA structures throughout the various steps of mitosis. Furthermore, we discuss the potential ways in which cells might not only tolerate this inevitable aspect of chromosome biology, but also exploit it to assist in the maintenance of genome stability.