This dissertation describes the development and application of surface-enhanced hyper-Raman scattering (SEHRS) as a nonlinear spectroscopic probe in three studies. The first study explores the measurement of SEHRS from short-wave infrared (SWIR) excitation sources. Ultrasensitive detection of the scattered signal, which occurs in a "biological transparent window," is accomplished for three analyte molecules under modest experimental conditions. These results demonstrate that SEHRS-based methods have compelling potential for chemical analysis and molecular imaging.The second study compares resonance hyper-Raman scattering of crystal violet from experimental SEHRS measurements and theoretical calculations over its two lowest-lying electronic states (12,700-27,400 cm-1). The qualitative agreement between theory and experiment indicates that first-principles calculations capture many of the complex resonance contributions in this prototypical octupolar system. The discrepancies between theory and experiment are investigated by comparing spectra obtained in different local environments as well as from higher-order surface-enhanced spectroscopies. A comparison between relative SEHRS band ratios plotted as a function of excitation wavelength and crystal violet's absorption spectra elucidates correlations between groups of vibrations and the excited-electronic states. The results suggest that the spectral features across the range of resonance excitation energies (~15,500-27,400 cm-1) are dominated by strong A-term scattering. The final study focuses on orientation effects in the SEHRS of rhodamine 6G on resonance with its lowest electronic state S1. First-principles calculations demonstrate the non-Condon effects that dominate resonance hyper-Raman scattering produce unique spectra depending on molecular orientation, thereby, making SEHRS a much more sensitive probe of adsorbate geometry than its linear counterpart, surface-enhanced Raman scattering. Comparisons between theoretical calculations and experimentally measured SEHRS from aggregated silver colloids reveal R6G adsorbs mostly perpendicular with the nanoparticle surface. The predicted geometry both agrees well with previous reports and adds significantly to our understanding of R6G's interactions with metal colloids.