The recent discovery of the accelerating expansion of the Universe and thus the existence of dark energy was made possible by the study of Type Ia supernovae. These thermonuclear explosions of white dwarfs are excellent standardizable candles that can be seen out to great distances and used to constrain cosmological parameters. However, in an era when modern surveys are discovering hundreds of Type Ia supernovae and upcoming surveys plan to find thousands more, we are no longer limited by statistics, but are now being limited by systematic uncertainties in supernova cosmology. Among these systematic uncertainties are the nature of the supernova progenitor and the effect of the environment on the progenitor. An excellent way to probe these systematics is through the study of the galaxies that host Type Ia supernovae. Correlations have been found between supernova properties and the physical properties of their host galaxies such as mass, metallicity, and star formation rate. In this dissertation, I use supernovae from the full three-year Sloan Digital Sky Survey II (SDSS-II) Supernova Survey and multi-wavelength photometry of their host galaxies to find evidence of a correlation between supernova luminosities and the age of their hosts, a possible proxy for progenitor age. I also detail a method of host galaxy identification, tested and applied to the many thousands of SDSS-II supernova candidates, which will be published in the upcoming final data release of the Supernova Survey. In addition, I present work in which I compute the luminosity functions for Type Ia supernovae and their host galaxies. This work and continuing work in this vein can help shed light on the nature of dark energy and improve the utility of Type Ia supernovae as cosmological distance indicators.