Surface plasmon polariton has attracted more and more attention in recent years, since it possesses the ability to break the optical diffraction limit and confine the electromagnetic field at sub-wavelength scale. Besides the investigations in classical regime, the rapidly developed quantum optics and quantum information technologies also provide a new perspective to investigate the surface plasmons at a quantum level, thus growing the new era for both quantum optics and plasmons. Among numerous kinds of nanostructures to support the quantum plasmons, silver nanowire (AgNW) has became one of the most popular and typical plasmonic one-dimensional waveguide. It has been widely used in the quantum information processing thanks to the mature preparation process and several natural advantages such as a single-crystal structure and relatively low absorption. On one hand, the quantum behaviors of the surface plasmon polaritons can be investigated experimentally on the silver nanowires; on the other hand, the silver nanowires can also severed as functional quantum devices to realize various applications in quantum information.Here, we review the progress of the representative theoretical and experimental works of quantum information processes using the surface plasmons on AgNWs from three aspects. First of all, we introduce the basic optical properties and the quantum properties of the surface plasmons on silver nanowires. The lower-order plasmon modes on silver nanowires have been shown, and it can be found that each of them possesses different polarization properties, electromagnetic field distributions, the abilities to confine the energy and other fundamental optical characteristics. Therefore it is of great importance to control and select the desired modes in specific researches. The influence of the substrate on the modes has also been discussed and shown to be non-negligible. For the quantum part, we introduce the early theories for quantizing plasmonic waves in metals, and many subsequent experiments which have demonstrated the wave-particle duality, non-classical statistical property, the property as Bosons and other quantum properties of the plasmons on the AgNWs. All of these important characteristics are the fundamental of the further applications of the silver nanowires in quantum information.Secondly, we have presented the applications of silver nanowires in the quantum information processing so far, which is the main part of the manuscript. We have summarized them into three application directions in detail. The first one is using the silver nanowires to couple with sorts of quantum single photon emitters. Nowadays most experimental works are within the weak coupling region and propose to modulate the radiation properties of the quantum single photon emitters, in order to further improve the performance or realize efficient collection. Meanwhile the strong coupling between the silver nanowire and emitters could dramatically enhance the nonlinear interactions, which has great potential for deterministic quantum manipulation. But to experimentally realize the strong coupling by AgNWs is still a challenge and most works remain theoretical proposals. Another trending research direction focuses on building the quantum plasmonic circuits with silver nanowires. Multiple kinds of plasmonic quantum states, including Fock states,polarization entangled states,NOON states and so on, have been generated and then propagate on silver nanowires. Linear and non-linear operations of the quantum plasmons through the cascade of the AgNWs have also been realized in many works. Several significant breakthroughs and latest developments are introduced, demonstrating the possibility of achieving a complete process, composed of the generations, operations and measurements of the quantum plasmons, in an integrated plasmonic circuit at nanoscale. The last potential application direction is using the quantum plasmons on AgNWs to improve the measurements and sensing. To combine the natural advantages of the plasmons for breaking the optical diffraction limit and the novel non-classical properties of the quantum states for breaking the shot noise limit, the AgNWs can transmit different quantum plasmonic states and served as quantum probes in sensing and measurements. Therefore, it provides a route to enhance the spatial resolution and sensitivities of the measurements at the same time. Though the experimental works in quantum sensing and quantum metrology with AgNWs are not as many as that of the aforementioned two directions, great potentials have been proved in sorts of present related works.Finally, we have pointed out some problems still waiting to be solved, and discussed the possible developments of the silver nanowires applying in quantum optics and quantum plasmons in the future. More studies on the effect of loss in quantum information process are needed, including to further decrease the loss, or utilize the loss itself of the silver nanowires. To construct hybrid systems integrated of the AgNWs with other nano-optical devices might be a practical way to balance the trade-off relationship between loss and binding. Other challenges such as to prevent the silver nanowires from oxidation, to experimentally achieve stronger coupling strength and more complicated circuits with AgNWs, also remain to be overcome. Further improving the experimental technology and investigating the preparation methods of AgNWs with special morphology could be helpful, and might offer novel insights into the quantum information. Besides, deeper understanding of the fundamental properties of the silver nanowires and the quantum plasmons would lead to a new frontier in quantum applications such as ultra-compact quantum integrated circuitry, single-photon sources with high performance, quantum sensing beyond the optical diffraction limit, etc.