Oesophageal adenocarcinoma (OAC) provides an ideal case study to characterize large-scale rearrangements. Using whole genome short-read sequencing of 383 cases, for which 214 had matched whole transcriptomes, we observed structural variations (SV) with a predominance of deletions, tandem duplications and inter-chromosome junctions that could be identified as LINE-1 mobile element (ME) insertions. Complex clusters of rearrangements resembling breakage-fusion-bridge cycles or extrachromosomal circular DNA accounted for 22% of complex SVs affecting known oncogenes. Counting SV events affecting known driver genes substantially increased the recurrence rates of these drivers. After excluding fragile sites, we identified 51 candidate new drivers in genomic regions disrupted by SVs, including ETV5, KAT6B and CLTC. RUNX1 was the most recurrently altered gene (24%), with many deletions inactivating the RUNT domain but preserved the reading frame, suggesting an altered protein product. These findings underscore the importance of identification of SV events in OAC with implications for targeted therapies.