In this thesis we perform theoretical investigations on the optical properties of geometrically infinite metallic nano-structures such as nanoparticle/film systems and periodic nanoparticle arrays. We apply both Plasmon Hybridization (PH) and Finite-Difference Time-Domain (FDTD) methods and we obtain quantitative agreement with experimental measurements as well as other theoretical methods such as Mie Theory and Finite Element simulation. For the nanoparticle over film structure, our research shows that the plasmonic interaction between the nanoparticle and the film is an electromagnetic analogue of the spinless Anderson-Fano model, which was used to describe the interaction of a localized electronic state with a continuous band of electronic states. Three characteristic regimes of the model are realized as the energy of the nanoparticle plasmon resonance lies above, within, or below the energy band of the surface plasmon state. These three interaction regimes are controlled by the film thickness. In the thin film limit, the plasmonic coupling between the nanoshell and the film induces a low-energy virtual state (VS) mainly composed of delocalized film, which can be further tuned as the aspect ratio of the nanoshell changes. The calculations are found to agree well with experimental measurements. Using FDTD method, we show that the electromagnetic field enhancement induced by the VS in the thin film limit can be very large and the nanoparticle/film system could serve as an ideal substrate for Surface Enhanced Raman Spectroscopy (SERS) and Tip Enhanced Raman Spectroscopy (TERS). The plasmonic properties of nanoparticle arrays are investigated using FDTD with Periodic Boundary Conditions (PBC). Our research shows that 2D hexagonal (hcp) nanoshell arrays possess ideal properties as a substrate that combines SERS and Surface Enhanced Infrared Absorption (SEIRA), with large electric field enhancements at the same spatial locations in the structure. With small interparticle distance and normal incidence, the multipolar plasmons of each constituent nanoshells hybridize and form band structures. For SERS, a relatively narrow near infrared (NIR) plasmon resonance is induced by the quadrupolar plasmonic interactions among neighboring nanoshells. For SEIRA, an extremely broad mid infrared (MIR) is induced by the dipolar resonances of the nanoshells. The relation between the field enhancements and the interparticle separation in the MIR regime is systematically investigated using an electrostatic model. We apply the Multiple Unit Cell (MUC) PBC implementation for calculating the optical properties of periodic nanoparticle arrays for oblique excitations using the Finite-Difference Time-domain method. We discuss computational and numerical aspects and present a detailed investigation of its convergence properties. We investigate the extinction spectra of one-dimensional metallic nanosphere arrays under different incident angles and polarizations. The dispersion relation of the transverse and the longitudinal plasmon modes are calculated and found to be in qualitative agreement with simple electrostatic models.