Nanometer-scale particles of the noble metals have been used for decades as contrast enhancement agents in electron microscopy. Over the past several years it has been demonstrated that these particles also function as excellent contrast agents for optical imaging techniques. The resonant optical scattering they exhibit enables scattering cross sections that may be many orders of magnitude greater than the analogous efficiency factor for fluorescent dye molecules. Biologically relevant labeling with nanoparticles generally results in aggregates containing a few to several tens of particles. The electrodynamic coupling between particles in these aggregates produces observable shifts in the resonance-scattering spectrum. This dissertation provides a theoretical analysis of the scattering from nanoparticle aggregates. The key objectives are to describe this scattering behavior qualitatively and to provide numerical codes usable for modeling its application to biomedical engineering. Considerations of the lowest-order dipole-dipole coupling lead to simple qualitative predictions of the behavior of the spectral properties of the optical cross sections as they depend on number of particles, inter-particle spacing, and aggregate aspect ratio. More comprehensive analysis using the multiple-particle T-matrix formalism allows the elaboration of more subtle cross-section spectral features depending on the interactions of the electrodynamic collective-modes of the aggregate, of individual-particle modes, and of modes associated with groups of particles within the aggregate sub-structure. In combination these analyses and the supporting numerical code-base provide a unified electrodynamic approach which facilitates interpretation of experimental cross section spectra, guides the design of new biophysical experiments using nanoparticle aggregates, and enables optimal fabrication of nanoparticle structures for biophysical applications. / text