abstract: Recent improvements in energy resolution for electron energy-loss spectroscopy in the scanning transmission electron microscope (STEM-EELS) allow novel effects in the low-loss region of the electron energy-loss spectrum to be observed. This dissertation explores what new information can be obtained with the combination of meV EELS energy resolution and atomic spatial resolution in the STEM. To set up this up, I review nanoparticle shape effects in the electrostatic approximation and compare the “classical” and “quantum” approaches to EELS simulation. Past the electrostatic approximation, the imaging of waveguide-type modes is modeled in ribbons and cylinders (in “classical" and “quantum" approaches, respectively), showing how the spatial variations of such modes can now be imaged using EELS. Then, returning to the electrostatic approximation, I present microscopic applications of low-loss STEM-EELS. I develop a “classical” model coupling the surface plasmons of a sharp metallic nanoparticle to the dipolar vibrations of an adsorbate molecule, which allows expected molecular signal enhancements to be quantified and the resultant Fano-type asymmetric spectral line shapes to be explained, and I present “quantum” modelling for the charged nitrogen-vacancy (NV-) and neutral silicon-vacancy (SiV0) color centers in diamond, including cross-sections and spectral maps from density functional theory. These results are summarized before concluding. Many of these results have been previously published in Physical Review B. The main results of Ch. 2 and Ch. 4 were packaged as “Enhanced vibrational electron energy-loss spectroscopy of adsorbate molecules” (99, 104110), and much of Ch. 5 appeared as “Prospects for detecting individual defect centers using spatially resolved electron energy loss spectroscopy” (100, 134103). The results from Ch. 3 are being prepared for a forthcoming article in the Journal of Chemical Physics. / Dissertation/Thesis / Doctoral Dissertation Physics 2020