Next-generation sequencing technology has enabled the comprehensive detection of genomic alterations in human somatic cells, including point mutations, chromosomal rearrangements, and structural variations (SVs). Using sophisticated bioinformatics algorithms, unbiased catalogs of SVs are emerging from thousands of human cancer genomes for the first time. Via careful examination of SV breakpoints at single-nucleotide resolution as well as local DNA copy number changes, diverse patterns of genomic rearrangements are being revealed. These "SV signatures" provide deep insight into the mutational processes that have shaped genome changes in human somatic cells. This review summarizes the characteristics of recently identified complex SVs, including chromothripsis, chromoplexy, microhomology-mediated breakage-induced replication (MMBIR), and others, to provide a holistic snapshot of the current knowledge on genomic rearrangements in somatic cells.