Triple-negative breast cancer (TNBC) and other molecularly heterogeneous malignancies present a significant clinical challenge due to a lack of high-frequency “driver” alterations amenable to therapeutic intervention. These cancers often exhibit genomic instability, resulting in chromosomal rearrangements that affect the structure and expression of protein-coding genes. However, identification of these rearrangements remains technically challenging. Using a newly developed approach that quantitatively predicts gene rearrangements in tumor-derived genetic material, we identified and characterized a novel oncogenic fusion involving the MER proto-oncogene tyrosine kinase (MERTK) and discovered a clinical occurrence and cell line model of the targetable FGFR3–TACC3 fusion in TNBC. Expanding our analysis to other malignancies, we identified a diverse array of novel and known hybrid transcripts, including rearrangements between noncoding regions and clinically relevant genes such as ALK, CSF1R, and CD274/PD-L1. The over 1,000 genetic alterations we identified highlight the importance of considering noncoding gene rearrangement partners, and the targetable gene fusions identified in TNBC demonstrate the need to advance gene fusion detection for molecularly heterogeneous cancers. Cancer Res; 76(16); 4850–60. ©2016 AACR.