Unlike traditional small-molecule agents, biopharmaceuticals, like synthetic RNAs, enzymes, and monoclonal antibodies, are highly vulnerable to environmental conditions. Preservation of their functional integrity necessitates advanced delivery methods. Being biocompatible, extracellular vesicles (EVs) gained attention as a promising system for delivering biopharmaceuticals, addressing challenges related to the stability and efficacy of sensitive therapeutic molecules. Indeed, EVs can cross biological barriers like the blood-brain barrier, delivering therapeutic cargo to tissues that are traditionally difficult to reach. Recent innovations in surface modification technologies, including ligand and antibody attachment, have further enhanced EVs' targeting capabilities, making them particularly effective in personalized medicine. Here, we review the versatile suitability of EVs for being next-generation delivery vehicles of biopharmaceuticals, including current standings, practical challenges, and possible future directions of the technology.