Recent research into structural variants (SVs) has established their importance to medicine and molecular biology, elucidating their role in various diseases, regulation of gene expression, ethnic diversity, and large-scale chromosome evolution—giving rise to the differences within populations and among species. Nevertheless, characterizing SVs and determining the optimal approach for a given experimental design remains a computational and scientific challenge. Multiple approaches have emerged to target various SV classes, zygosities, and size ranges. Here, we review these approaches with respect to their ability to infer SVs across the full spectrum of large, complex variations and present computational methods for each approach.