SWI/SNF chromatin remodelling complexes use the energy of ATP hydrolysis to remodel nucleosomes and to modulate transcription. Growing evidence indicates that these complexes have a widespread role in tumour suppression, as inactivating mutations in several SWI/SNF subunits have recently been identified at a high frequency in a variety of cancers. However, the mechanisms by which mutations in these complexes drive tumorigenesis are unclear. In this Review we discuss the contributions of SWI/SNF mutations to cancer formation, examine their normal functions and discuss opportunities for novel therapeutic interventions for SWI/SNF-mutant cancers.