Somatically acquired genomic rearrangements are common genomic alterations that contribute to malignancy by altering the expression or activity of cancer-related genes in human cancer. Genomic rearrangements play a crucial role in tumor development by contributing to driver events in approximately 25% of cancer patients. Most rearrangements are nonrecurrent and lack functional impact. However, some rearrangements produce functional transcripts and act as cancer drivers that may be therapeutic targets. The growing availability of whole-genome and matched RNA-sequencing data from large patient cohorts offers tremendous opportunities to identify novel, clinically relevant drivers arising from genomic rearrangements. In this review, we summarize current knowledge of driver rearrangements as therapeutic targets and highlight recent discoveries of functional transcripts such as intergenic fusions generated by noncanonical rearrangements. We also discuss computational approaches to decode rearrangement patterns and leverage large-scale whole-genome data to discover novel drivers.