With the advent of next-generation sequencing technologies, we have witnessed a rapid pace of discovery of new patterns of somatic structural variation in cancer genomes, and an attempt to figure out their underlying mechanisms. Some of these mechanisms are associated with particular cancer types, and in some cases are the main cause of the structural mutations that drive the oncogenic process. This review provides an overview of the patterns of somatic structural variation and chromosomal structures that characterize cancer genomes, their causal mechanisms and their impact in oncogenesis.