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Although several recent studies have characterized structural variants (SVs) in germline and cancer genomes independently, the genomic contexts of these SVs have not been comprehensively compared. We examined similarities and differences between 2 million germline and 115 thousand tumor SVs from a cohort of 963 patients from The Cancer Genome Atlas. We found significant differences in features related to their genomic sequences and localization that suggest differences between SV-generating processes and selective pressures. For example, our results show that features linked to transposon-mediated processes are associated with germline SVs, while somatic SVs more frequently show features characteristic of chromoanagenesis. These genomic differences enabled us to develop a classifier-the Germline and Tumor Structural Variant or "the great GaTSV" -that accurately distinguishes between germline and cancer SVs in tumor samples that lack a matched normal sample.