Nucleic acid drugs, such as siRNAs, antisense oligonucleotides, and miRNAs, exert their therapeutic effects by causing genetic changes in cells. However, there are various limitations in their delivery to target organs and cells, making their application to cancer treatment difficult. Extracellular vesicles (EVs) are lipid bilayer particles that are released from most cells, are stable in the blood, and have low immunogenicity. Methods using EVs to deliver nucleic acid drugs to target organs are rapidly being developed that take advantage of these properties. There are two main methods for loading nucleic acid drugs into EVs. One is to genetically engineer the parent cell and load the target gene into the EV, and the other is to isolate EVs and then load them with the nucleic acid drug. Target organ delivery methods include passive targeting using the enhanced permeation and retention effect of EVs and active targeting in which EVs are modified with antibodies, peptides, or aptamers to enhance their accumulation in tumors. In this review, we summarize the advantages of EVs as a drug delivery system for nucleic acid drugs, the methods of loading nucleic acid drugs into EVs, and the targeting of EVs to target organs.