Polyploid cells contain multiple copies of all chromosomes. Polyploidization can be developmentally programmed to sustain tissue barrier function or to increase metabolic potential and cell size. Programmed polyploidy is normally associated with terminal differentiation and poor proliferation capacity. Conversely, non-programmed polyploidy can give rise to cells that retain the ability to proliferate. This can fuel rapid genome rearrangements and lead to diseases like cancer. Here, the mechanisms that generate polyploidy are reviewed and the possible challenges upon polyploid cell division are discussed. The discussion is framed around a recent study showing that asynchronous cell cycle progression (an event that is named "chronocrisis") of different nuclei from a polyploid cell can generate DNA damage at mitotic entry. The potential mechanisms explaining how mitosis in non-programmed polyploid cells can generate abnormal karyotypes and genetic instability are highlighted.