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The use of a solid dispersion (SD), a mixture of an active pharmaceutical ingredient and a polymer excipient, may significantly enhance the aqueous solubility and oral bioavailability of a hydrophobic drug, but the role of the polymer is poorly understood. For example, hydroxypropyl methylcellulose acetate succinate (HPMCAS) is considered to be one of the best performing excipients, but its effectiveness is not universal to all drugs. Elucidation of the critical properties of HPMCAS is inhibited due to the poor spatial resolution and sensitivity of the techniques traditional used to characterize SDs. To address this shortcoming, the studies in this dissertation focus on the development of novel analytical methods for characterizing SDs in both the solid-state and during dissolution. First, transmission electron microscopy (TEM) and electron diffraction evaluates drug crystallinity in SDs with a spatial resolution and sensitivity superior to the traditional methods. Second, energy-dispersive X-ray spectroscopy probes the spatial distribution of drug and polymer in a SD particle. Third, electron energy-loss spectroscopy quantitatively measures the concentration of drug and polymer in a SD with both high concentration and spatial resolution. Fourth, cryogenic TEM and small-angle X-ray scattering reveal a direct correlation between SD dissolution and nanostructure evolution in solution. Finally, the utility of these novel tools and possible future research directions are discussed.