Plasmonics, focusing on the fundamental researches and novel applications of plasmons, has rapidly developed as an important branch of nano-optics in recent years. Essentially, surface plasmons are highly localized collective electron excitation at a metal-dielectric interface. This elementary excitation can be strongly coupled with electromagnetic fields, which enable one to collect, manipulate, and emit micron-scale optical signals through using nano-scale structures. Recently, the quantum properties of plasmons have received tremendous attention as nanofabrication techniques approach to the quantum limit. On this scale, with the unique intrinsic properties of plasmons, i.e. the particle-like nature of photons and wave-like nature of electrons, quantum plasmonics exhibits very attractive prospects in quantum information, high-efficiency optoelectronic devices, and highly sensitive detection, etc. Here in this paper, we review the development of quantum plasmonics in recent years, by introducing the research progress of relevant theories and the experimental breakthroughes. Some perspectives of the future development of quantum plasmonics are also outlined.