Genome editing using the clustered regularly interspaced short palindromic repeats (CRISPR) and CRISPR-associated protein (Cas) gene-editing system (CRISPR-Cas) is a valuable tool for fundamental and applied research applications. Significant improvements in editing efficacy have advanced genome editing strategies into phase 3 human clinical trials. However, recent studies suggest that our understanding of editing outcomes has lagged behind the developments made in generating the edits themselves. While many researchers have analyzed on- and off-target events through the lens of small insertions or deletions at predicted sites, screens for larger structural variants (SVs) and chromosomal abnormalities are not routinely performed. Full and comprehensive validation of on- and off-target effects is required to ensure reproducibility and to accurately assess the safety of future editing applications. Here we review SVs associated with CRISPR-editing in cells of human origin and highlight the methods used to detect and avoid them.