Extracellular vesicles (EVs) are natural micro-/nanoparticles that play an important role in intercellular communication. They are secreted by producer/donor cells and subsequent uptake by recipient/acceptor cells may result in phenotypic changes in these cells due to the delivery of cargo molecules, including lipids, RNA, and proteins. The process of endocytosis is widely described as the main mechanism responsible for cellular uptake of EVs, with endosomal escape of cargo molecules being a necessity for the functional delivery of EV cargo. Equivalent to synthetic micro-/nanoparticles, the properties of EVs, such as size and composition, together with environmental factors such as temperature, pH, and extracellular fluid composition, codetermine the interactions of EVs with cells, from binding to uptake, intracellular trafficking, and cargo release. Innovative assays for detection and quantification of the different steps in the EV formation and EV-mediated cargo delivery process have provided valuable insight into the biogenesis and cellular processing of EVs and their cargo, revealing the occurrence of EV recycling and degradation, next to functional cargo delivery, with the back fusion of the EV with the endosomal membrane standing out as a common cargo release pathway. In view of the significant potential for developing EVs as drug delivery systems, this review discusses the interaction of EVs with biological membranes en route to cargo delivery, highlighting the reported techniques for studying EV internalization and intracellular trafficking, EV-membrane fusion, endosomal permeabilization, and cargo delivery, including functional delivery of RNA cargo.