In cavity quantum electrodynamics, when the interaction between quantum emitter and cavity mode is strong enough to overcome the mean decay rate of the system, it will enter into a strong coupling regime, thereby forming part-light part-matter polariton states. Strong coupling can serve as a promising platform for room temperature Bose-Einstein condensation, polariton lasing, single photon nonlinearity, quantum information, etc. Localized surface plasmons supported by single metal nanostructures possess extremely small mode volume, which is favorable for realizing strong coupling. Moreover, the nanoscale dimensions of plasmonic structures can facilitate the miniaturization of strong coupling systems. Here, the research progress of strong plasmon-exciton coupling between single metal nanoparticles/nanogaps and quantum emitters is reviewed. The theory background of strong coupling is first introduced, including quantum treatment, classical coupled oscillator model, as well as the analytical expressions for scattering and photoluminescence spectra. Then, strong coupling between different kinds of plasmonic nanostructures and quantum emitters is reviewed. Single metal nanoparticles, nanoparticle dimers, and nanoparticle-on-mirror structures constitute the most typical plasmonic nanostructures. The nanogaps in the latter two systems can highly concentrate electromagnetic field, providing optical nanocavities with smaller mode volume than single nanoparticles. Therefore, the larger coupling strength can be achieved in the nanogap systems, which is conducive to strong coupling at the single-exciton level. In addition, the active tuning of strong coupling based separately on thermal, electrical and optical means are reviewed. The energy and oscillator strength of the excitons in transition metal dichalcogenide (TMDC) monolayers are dependent on temperature. Therefore, the strong coupling can be tuned by heating or cooling the system. The excitons in TMDC monolayers can also be tuned by electrical gating, enabling electrical control of strong coupling. Optically tuning the quantum emitters provides another way to actively control the strong coupling. Overall, the research on active tuning of strong plasmon-exciton coupling is still very limited, and more investigations are needed. Finally, this review is concluded with a short summary and the prospect of this field.