Human genomes are continuously subjected to mutations, which can drive genetic diseases and cancer. An intriguing recent finding has been the discovery of chromothripsis, a spectacular and complex form of chromosome rearrangement that can occur in the genomes of cancer cells and patients with congenital diseases. Chromothripsis has been described in a large array of human cancers and various types of chromothripsis have appeared, which differ in complexity and genomic hallmarks. From the combined genomic data a consensus hypothesis has been inferred, involving aberrant DNA replication and chromosome shattering as the underlying processes explaining chromothripsis. In addition, recent work has established several cellular models that recapitulate chromothripsis under defined experimental conditions. One of these models indicates that chromothripsis can originate from DNA damage in micronuclei, providing an elegant explanation for the restriction of chromothriptic rearrangements to a single chromosome. Alternatively, chromothripsis can be caused by telomere crisis, a process that involves formation of dicentric chromosomes and chromatin bridges. Here, we summarize the genomic features of chromothripsis and we discuss experimental approaches that allow dissection of the chromothripsis process.