As a major branch of nanophotonics, plasmonics often concerns how light interacts with the electron oscillations in nanostructured metals. This interaction gives rise to the strong confinement of electromagnetic fields both spatially and temporally, leading to a myriad of new applications, such as wave guiding, sensing, imaging, energy harvesting and conversion. On the one hand, nanoscale plasmonic systems have provided an excellent platform for studying nonclassical effects, such as spatial nonlocality, electron spill-out, plasmon-exciton strong coupling and quantum tunneling etc. On the other hand, the strong field enhancement in the plasmonic systems can generate giant nonlinear responses, such as high-harmonic wave generation, Kerr nonlinearity, and optical rectification. In this context, the field of plasmonics nanophotonics can be substantially enriched and further developed by incorporating the nonclassical and nonlinear effects.