Type Ia Supernovae have provided a powerful tool for measuring the accelerating expansion of the Universe, and current and planned surveys will eliminate any significant source of statistical uncertainty at medium-range redshifts. However, the persistent presence of intrinsic dispersion in supernova magnitudes indicates latent unmodeled processes, which can lead to systematic bias in the standardized magnitudes and hence in the measurement of cosmological parameters. In this talk I will discuss methods for improving the precision of Type Ia supernovae as cosmological indicators through the use of better models for their behavior. In particular I will discuss the development and performance of the new supernova model SNEMO, and show how it can be used to improve the cosmological constraints from existing supernova samples. Additionally, I will give an overview of the supernova survey underway with the Subaru Strategic Program and show how it is being used to efficiently fill in the high-redshift region of the Hubble diagram.