Electron energy loss spectroscopy (EELS) performed in a scanning transmission electron microscope (STEM) has demonstrated unprecedented power in the characterization of surface plasmons. The subangstrom spatial resolution achieved in EELS and its capability of exciting the full set of localized surface plasmon resonance (LSPR) modes supported by a metallic nanostructure makes STEM/EELS an ideal tool in the study of LSPRs. The plasmonic properties characterized using EELS can be associated with geometric or structural features collected simultaneously in a STEM to achieve a deeper understanding of the plasmonic response. In this review, we provide the reader a thorough experimental description of EELS as a LSPR characterization tool and summarize the exciting recent progress in the field of STEM/EELS plasmon characterization.