In this review article, we provide an overview of recent research activities in the study of plasmonic optical properties of metal nanostructures with emphasis on understanding the relation between surface plasmon absorption and structure. Both experimental results and theoretical calculations have indicated that the plasmonic absorption strongly depends on the detailed structure of the nanomaterials. Examples discussed include spherical nanoparticles, nanorods, nanowires, hollow nanospheres, aggregates, and nanocages. Plasmon-phonon coupling measured from dynamic studies as a function of particle size, shape, and aggregation state is also reviewed. The fascinating optical properties of metal nanostructures find important applications in a number of technological areas including surface plasmon resonance, surface-enhanced Raman scattering, and photothermal imaging and therapy. Their novel optical properties and emerging applications are illustrated using specific examples from recent literature. The case of hollow nanosphere structures is highlighted to illustrate their unique features and advantages for some of these applications.