Telomere crisis occurs during tumorigenesis when depletion of the telomere reserve leads to frequent telomere fusions. The resulting dicentric chromosomes have been proposed to drive genome instability. Here, we examine the fate of dicentric human chromosomes in telomere crisis. We observed that dicentric chromosomes invariably persisted through mitosis and developed into 50–200 μm chromatin bridges connecting the daughter cells. Before their resolution at 3–20 hr after anaphase, the chromatin bridges induced nuclear envelope rupture in interphase, accumulated the cytoplasmic 3′ nuclease TREX1, and developed RPA-coated single stranded (ss) DNA. CRISPR knockouts showed that TREX1 contributed to the generation of the ssDNA and the resolution of the chromatin bridges. Post-crisis clones showed chromothripsis and kataegis, presumably resulting from DNA repair and APOBEC editing of the fragmented chromatin bridge DNA. We propose that chromothripsis in human cancer may arise through TREX1-mediated fragmentation of dicentric chromosomes formed in telomere crisis. Display omitted •Dicentric chromosomes formed during telomere crisis do not break in mitosis•Cells with dicentrics develop chromatin bridges that induce nuclear envelope rupture•The TREX1 3′ nuclease generates ssDNA in the bridges and facilitates their resolution•Post-telomere crisis cells often show chromothripsis and kataegis During telomere crisis, dicentric chromosomes form long chromatin bridges that induce nuclear envelope rupture. Nucleolytic attack of the dicentric chromosomes generates extensive ssDNA and leads to bridge breakage, which may contribute to the occurrence of chromothripsis and kataegis in cancer genomes.