Noble metal nanostructures possess unique properties including large near-field enhancement and strong light scattering and absorption due to their plasmon resonance - the collective coherent oscillation of the metal free electrons in resonance with the electromagnetic field of light. The effect of nanostructure size, shape, composition, and environment on the plasmon resonance frequency and plasmonic enhancement is well known. In this thesis, we describe the effect of inter-particle coupling in assembled plasmonic nanostructures on their radiative and non-radiative properties. When metal nanoparticles assemble, plasmon oscillations of neighboring particles couple, resulting in a shift in the plasmon resonance frequency. Our investigation of plasmon coupling in gold nanorods shows that the coupling between the plasmons is "bonding" in nature when the plasmon oscillations are polarized along the inter-particle axis, whereas an "anti-bonding" interaction results when the polarization is perpendicular. We studied the distance-dependence of plasmon coupling using electrodynamic simulations and experimental plasmon resonances of lithographically fabricated gold nanoparticle pairs with systematically varying inter-particle separations. The strength of plasmon bonding, reflected by the fractional plasmon shift, decays near-exponentially with the inter-particle separation (in units of particle size) according to a universal trend independent of the nanoparticle size, shape, metal type, or medium. From the universal scaling model, we obtain a "plasmon ruler equation" which calculates (in good agreement with the experiments of Alivisatos and Liphardt) the inter-particle separation in a gold nanosphere pair from its plasmon resonance shift, making it applicable to the determination of inter-site distances in biological systems. Universal size-scaling is valid also in the metal nanoshell structure, a nanosphere trimer, and pairs of elongated nanoparticles, thus making it a generalized fundamental model, which is useful in optimizing plasmon coupling for achieving tunable plasmon resonances, enhanced plasmonic sensitivities, and large SERS cross-sections. Ultrafast laser pump-probe studies of non-radiative electronic relaxation in coupled metal nanospheres in aggregates and in gold nanospheres conjugated to thiol SAMs are also reported. We also show that the relative contribution of scattering (radiative) to absorption (non-radiative) part of the plasmon relaxation, respectively useful in optical and photothermal applications, can be increased by increasing the nanostructure size.