Localized surface plasmon resonance (LSPR) spectroscopy of metallic nanoparticles is a powerful technique for chemical and biological sensing experiments. Moreover, the LSPR is responsible for the electromagnetic-field enhancement that leads to surface-enhanced Raman scattering (SERS) and other surface-enhanced spectroscopic processes. This review describes recent fundamental spectroscopic studies that reveal key relationships governing the LSPR spectral location and its sensitivity to the local environment, including nanoparticle shape and size. We also describe studies on the distance dependence of the enhanced electromagnetic field and the relationship between the plasmon resonance and the Raman excitation energy. Lastly, we introduce a new form of LSPR spectroscopy, involving the coupling between nanoparticle plasmon resonances and adsorbate molecular resonances. The results from these fundamental studies guide the design of new sensing experiments, illustrated through applications in which researchers use both LSPR wavelength-shift sensing and SERS to detect molecules of chemical and biological relevance.