Several recent studies have reported unexpected correlations between the properties of Type Ia supernovae and their host galaxies. For example, the slope of the empirical brightness-color relation used to standardize SNe Ia appears to be smaller for SNe hosted by passive galaxies than for those hosted by star-forming galaxies. More massive galaxies and those with less star formation also appear to host brighter SNe Ia, after standard light curve shape and color corrections are applied. In this talk, I will discuss how the correlated properties of SNe Ia and their hosts offer opportunities to improve the efficiency and accuracy of SN surveys, particularly at high redshift. At the end of the talk, I will describe an ongoing program to use high signal-to-noise ratio Keck spectroscopy of nearby SN Ia hosts to pinpoint the underlying physics of host-galaxy -- SN correlations.