Chromosomal rearrangements are generally thought to accumulate gradually over many generations. However, DNA sequencing of cancer and congenital disorders uncovered a new pattern in which multiple rearrangements arise all at once. The most striking example, chromothripsis, is characterized by tens or hundreds of rearrangements confined to a single chromosome or to local regions over a few chromosomes. Genomic analysis of chromothripsis and the search for its biological mechanism have led to new insights on how chromosome segregation errors can generate mutagenesis and changes to the karyotype. Here, we review the genomic features of chromothripsis and summarize recent progress on understanding its mechanism. This includes reviewing new work indicating that one mechanism to generate chromothripsis is through the physical isolation of chromosomes in abnormal nuclear structures (micronuclei). We also discuss connections revealed by recent genomic analysis of cancers between chromothripsis, chromosome bridges, and ring chromosomes.