Genome editing technology has emerged as a potential therapeutic tool for treating incurable diseases. In particular, the discovery of clustered regularly interspaced short palindromic repeats (CRISPR)/Cas systems and the design of single-guide RNAs (sgRNAs) have revolutionized genome editing applications. Unfortunately, compared with the rapid development of gene-editing tools, the progress in the development of delivery technologies is lagging behind and thus limiting the clinical application of genome editing. To overcome these limitations, researchers have investigated various delivery systems, including viral and non-viral vectors for delivering CRISPR/Cas and sgRNA complexes. As natural endogenous nanocarriers, extracellular vesicles (EVs) present advantages of biocompatibility, low immunogenicity, stability, and high permeability, making them one of the most promising drug delivery vehicles. This review provides an overview of the fundamental mechanisms of EVs from the aspects of biogenesis, trafficking, cargo delivery, and function as nanotherapeutic agents. We also summarize the latest trends in EV-based CRISPR/Cas delivery systems and discuss the prospects for future development. In particular, we put our emphasis on the state-of-the-art engineering strategies to realize efficient cargo packaging and loading. Altogether, EVs hold promise in bridging genome editing in the laboratory and clinical applications of gene therapies by providing a safe, effective, and targeted delivery vehicle.