Genome-editing technology has emerged as a potential tool for treating incurable diseases for which few therapeutic modalities are available. In particular, discovery of the clustered regularly interspaced short palindromic repeats (CRISPR)/Cas system together with the design of single-guide RNAs (sgRNAs) has sparked medical applications of genome editing. Despite the great promise of the CRISPR/Cas system, its clinical application is limited, in large part, by the lack of adequate delivery technology. To overcome this limitation, researchers have investigated various systems, including viral and nonviral vectors, for delivery of CRISPR/Cas and sgRNA into cells. Among nonviral delivery systems that have been studied are nanovesicles based on lipids, polymers, peptides, and extracellular vesicles. These nanovesicles have been designed to increase the delivery of CRISPR/Cas and sgRNA through endosome escape or using various stimuli such as light, pH, and environmental features. This review covers the latest research trends in nonviral, nanovesicle-based delivery systems that are being applied to genome-editing technology and suggests directions for future progress.