Cancer genome sequencing has identified chromothripsis, a complex class of structural genomic rearrangements involving the apparent shattering of an individual chromosome into tens to hundreds of fragments. An initial error during mitosis, producing either chromosome mis-segregation into a micronucleus or chromatin bridge interconnecting two daughter cells, can trigger the catastrophic pulverization of the spatially isolated chromosome. The resultant chromosomal fragments are religated in random order by DNA double-strand break repair during the subsequent interphase. Chromothripsis scars the cancer genome with localized DNA rearrangements that frequently generate extensive copy number alterations, oncogenic gene fusion products, and/or tumor suppressor gene inactivation. Here we review emerging mechanisms underlying chromothripsis with a focus on the contribution of cell division errors caused by centromere dysfunction.