Developments in semiconductor and laser technologies have facilitated development of terahertz (THz)-frequency (˜2-200 cm-1) technologies. Results published in the literature as far back as the early 20th century demonstrate the utility of this frequency range for myriad applications, but the improved performance of modern THz technologies has renewed interest in THz-frequency analysis. Material presented in this dissertation focuses on three applications of terahertz time-domain spectroscopy (THz-TDS): quantitation of gas-phase molecular species, analysis of polymeric materials, and investigation of dental tissue/composite structures. Gas phase species were quantified individually at concentrations ranging from several parts per million to several parts per thousand using various chemometric methods. Quantitative model robustness was evaluated by comparison of model precision, and partial least-squares (PLS) regressions provided the greatest precision. Species were quantified in mixtures using PLS with errors of prediction below the permissible exposure limits (PELs) set by the Occupational Safety and Health Administration. The effect of spectral broadening as a result of overall sample pressure was investigated, and species were analyzed in mixtures at various overall pressures. Errors of prediction were again near or below the PELs, demonstrating the utility of this method for atmospheric analysis. Chemical selectivity available in THz spectral features was evaluated and compared to selectivity available in infrared frequencies. Spectral parameters measured in the THz frequency range also provide insight into structural properties of polymeric materials. In some cases, spectral peaks may be used to identify the temperature at which phase changes occur within these materials. THz refractive index spectra were found to be a sensitive and non-destructive tool for identification of phase transition temperatures. The time-resolved measurement of THz-TDS makes it particularly useful for rapid, non-destructive analysis of layered structures. Ordinarily, the strength of bonds between dental tissues and composite materials are evaluated in the laboratory using destructive failure analyses. Transparency of dental tissues and composite materials used for restorative procedures to THz pulses allows investigation of interfaces between these materials. Refractive index spectra indicate locations in which delamination has occurred between bonded layers. These results provide an overview of unique capabilities of the THz-TDS method in real-life spectral analyses.