Chromothripsis and kataegis are frequently observed in cancer and may arise from telomere crisis, a period of genome instability during tumorigenesis when depletion of the telomere reserve generates unstable dicentric chromosomes1-5. Here we examine the mechanism underlying chromothripsis and kataegis by using an in vitro telomere crisis model. We show that the cytoplasmic exonuclease TREX1, which promotes the resolution of dicentric chromosomes4, plays a prominent role in chromothriptic fragmentation. In the absence of TREX1, the genome alterations induced by telomere crisis primarily involve breakage-fusion-bridge cycles and simple genome rearrangements rather than chromothripsis. Furthermore, we show that the kataegis observed at chromothriptic breakpoints is the consequence of cytosine deamination by APOBEC3B. These data reveal that chromothripsis and kataegis arise from a combination of nucleolytic processing by TREX1 and cytosine editing by APOBEC3B.