Genetic abnormalities are present in all tumor types, although the frequency and type can vary. Chromosome abnormalities include highly aberrant structures, particularly chromothriptic chromosomes. The generation of massive sequencing data has illuminated the scope of the mutational burden in cancer genomes, identifying patterns of mutations (mutation signatures), which have the potential to shed light on the relatedness and etiologies of cancers and impact therapy response. Some mutation patterns are clearly attributable to disruptions in pathways that maintain genomic integrity. Here we review recent advances in our understanding of genetic changes occurring in cancers and the roles of genome maintenance pathways.