With the development of nanotechnology, many new optical phenomena in nanoscale have been demonstrated. Through the coupling of optical waves and collective oscillations of free electrons in metallic nanostructures, surface plasmon polaritons can be excited accompanying a strong near field enhancement that decays in a subwavelength scale, which have potential applications in the surface-enhanced Raman scattering, biosensor, optical communication, solar cells, and nonlinear optical frequency mixing. In the present article, we review the Green's matrix method for solving the surface plasmon resonances and near field in arbitrarily shaped nanostructures and in binary metallic nanostructures. Using this method, we design the plasmonic nanostructures whose resonances are tunable from the visible to near-infrared, study the interplay of plasmon resonances, and propose a new way to control plasmonic resonances in binary metallic nanostructures. Near field concerns the evanescent wave bound to a nanostructured material surface that decays exponentially within a subwavelength [1,2]. At the metallic-dielectric interface or in the isolated metallic nanostructure, due to the existence of collective oscillations of free electrons, surface plasmons [3][4][5] are excited and are accompanied with the enhancement of optical near field. The large near field at the surface comes from the electric field carried by the metal, which is optimized by a proper matching of the geometry, the incident light, the metallic electric permittivity and dielectric environment. Nanostructures of noble metals strongly scatter and absorb light when the surface plasmon resonance (SPR) is excited [6]. The resonance frequency and intensity are dominated by the distribution of the polarization charge across the nanostructure [7]. This resonant enhancement has promoted many important applications, such as surface-enhanced Raman scattering [8], *Corresponding author (email: qhgong@pku.edu.cn) biosensors and nanometer plasmonic waveguides [9-12], optical antennas [13], solar cells [14,15], nonlinear optical frequency mixing [16][17][18] and so on.Currently, we can see a rapidly expanding array of metallic nanostructures. With the development of nanofabrication and nanolithography techniques, various metallic nanoparticles, such as nanospheres, nanoshells, nanorices, nanorings, nanostars, nanocages and nanotriangles, have been successfully fabricated [9]. For the nanostructures smaller than the electron mean-free path of the bulk metal, the dielectric permittivity becomes position-dependent. Generally, when the scale of nanostructure is larger than 10 nm, dielectric permittivity is approximately looked as position-independent. Nanorods and nanostrips have attracted particular attention because the longitudinal plasmon absorption bands are tunable with their aspect ratio changing from visible to near-infrared [19][20][21]. Xia and coworkers have managed to synthesize 100-nm-length nanobars and studied their scattering spectra [22]. Due to the adjustability