Metallic nanostructures support resonant oscillations of their conduction band electrons called localized surface plasmon resonances. Plasmons couple efficiently to light and have enabled a new class of technology for the manipulation of light at the nanoscale. Nanostructures that support plasmon resonances have the potential for a wide range of applications such as enhanced optical spectroscopy techniques for chemical- and bio-sensing, cancer diagnosis and therapy, metamaterials, and energy harvesting. As the field of plasmonics has progressed, these applications have become more sophisticated, requiring increasingly complex nanostructures. For example, coupled nanostructures of two or more nanoparticles are used extensively in plasmon-enhanced spectroscopy techniques because they exhibit extremely large optical field enhancements. Asymmetric nanostructures, such as nanocups (metallic semishells), have been shown to support magnetic modes that could be used in metamaterials applications. This class of complex plasmonic nanostructures holds great potential for both the observation of new physical phenomena and practical applications. This thesis will focus on the fabrication and characterization of several examples of these complex nanostructures using darkfield spectroscopy. The plasmon modes of a dimer consisting of two nanoshells are investigated in both the separated and conductively overlapping regimes and are interpreted using the plasmon hybridization model. Next, coupled nanoclusters of seven particles arranged in a hexagonal pattern are studied. It is found that these nanoclusters support Fano resonances due to the coupling and interference of degenerate subradiant and superradiant plasmon modes. These structures are found to have an extremely high sensitivity to the local dielectric environment, making them attractive for biosensing applications. Variations on the nanocluster geometry are then explored, and it is observed that by adding more particles and varying their sizes, the lineshape of the Fano resonance can be precisely engineered. The underlying subradiant and superradiant modes are then analyzed using cathodoluminescence imaging and spectroscopy. Finally the plasmon modes of asymmetric nanostructures are measured. Nanoeggs (nanoshells with an offset core) and nanocups (metallic semishells) are fabricated by electron beam induced ablation, and their plasmon modes are measured. The plasmon modes of nanocups are studied in detail, and nanocups are found to support both electric and magnetic plasmons.