Structural variation, composed of balanced and unbalanced genomic rearrangements, is an important contributor to human genetic diversity with prominent roles in somatic and congenital disease. At the nucleotide level, structural variants (SVs) have been shown to frequently harbor additional breakpoints and copy-number imbalances, a complexity predicted to emerge wholly as a single-cell division event. Chromothripsis, chromoplexy, and chromoanasynthesis, collectively referred to as chromoanagenesis, are three major mechanisms that explain the occurrence of complex germline and somatic SVs. While chromothripsis and chromoplexy have been shown to be key signatures of cancer, chromoanagenesis has been detected in numerous cases of developmental disease and phenotypically normal individuals. Such observations advocate for a deeper study of the polymorphic and pathogenic properties of complex germline SVs, many of which go undetected by traditional clinical molecular and cytogenetic methods. This review focuses on congenital chromoanagenesis, mechanisms leading to occurrence of these complex rearrangements, and their impact on chromosome organization and genome function. We highlight future applications of routine screening of complex and balanced SVs in the clinic, as these represent a potential and often neglected genetic disease source, a true ''iceberg under water.''