Abstract Background Fusion genes are typically identified by RNA sequencing (RNA-seq) without elucidating the causal genomic breakpoints. However, non–poly(A)-enriched RNA-seq contains large proportions of intronic reads that also span genomic breakpoints. Results We have developed an algorithm, Dr. Disco, that searches for fusion transcripts by taking an entire reference genome into account as search space. This includes exons but also introns, intergenic regions, and sequences that do not meet splice junction motifs. Using 1,275 RNA-seq samples, we investigated to what extent genomic breakpoints can be extracted from RNA-seq data and their implications regarding poly(A)-enriched and ribosomal RNA–minus RNA-seq data. Comparison with whole-genome sequencing data revealed that most genomic breakpoints are not, or minimally, transcribed while, in contrast, the genomic breakpoints of all 32 TMPRSS2-ERG–positive tumours were present at RNA level. We also revealed tumours in which the ERG breakpoint was located before ERG, which co-existed with additional deletions and messenger RNA that incorporated intergenic cryptic exons. In breast cancer we identified rearrangement hot spots near CCND1 and in glioma near CDK4 and MDM2 and could directly associate this with increased expression. Furthermore, in all datasets we find fusions to intergenic regions, often spanning multiple cryptic exons that potentially encode neo-antigens. Thus, fusion transcripts other than classical gene-to-gene fusions are prominently present and can be identified using RNA-seq. Conclusion By using the full potential of non–poly(A)-enriched RNA-seq data, sophisticated analysis can reliably identify expressed genomic breakpoints and their transcriptional effects.